%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ALG261^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:08:41 AM UTC 2026
% Result : Theorem 1.19s 0.39s
% Output : CNFRefutation 1.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 114
% Syntax : Number of formulae : 614 ( 284 unt; 0 typ; 113 def)
% Number of atoms : 4462 (1787 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 10530 ( 785 ~;1445 |; 7 &;7112 @)
% ( 2 <=>;1179 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 537 ( 537 >; 0 *; 0 +; 0 <<)
% Number of symbols : 174 ( 171 usr; 115 con; 0-4 aty)
% Number of variables : 2184 ( 39 ^;2140 !; 5 ?;2184 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_subst,type,
subst: $tType ).
thf(tp_term,type,
term: $tType ).
thf(tp_ap,type,
ap: term > term > term ).
thf(tp_apinj1,type,
apinj1: $o ).
thf(tp_apinj2,type,
apinj2: $o ).
thf(tp_apnotvar,type,
apnotvar: $o ).
thf(tp_axabs,type,
axabs: $o ).
thf(tp_axapp,type,
axapp: $o ).
thf(tp_axassoc,type,
axassoc: $o ).
thf(tp_axclos,type,
axclos: $o ).
thf(tp_axidl,type,
axidl: $o ).
thf(tp_axidr,type,
axidr: $o ).
thf(tp_axmap,type,
axmap: $o ).
thf(tp_axscons,type,
axscons: $o ).
thf(tp_axshiftcons,type,
axshiftcons: $o ).
thf(tp_axvarcons,type,
axvarcons: $o ).
thf(tp_axvarid,type,
axvarid: $o ).
thf(tp_axvarshift,type,
axvarshift: $o ).
thf(tp_comp,type,
comp: subst > subst > subst ).
thf(tp_hoasap,type,
hoasap: subst > term > subst > term > term ).
thf(tp_hoasapinj1,type,
hoasapinj1: $o ).
thf(tp_hoasapinj1_gthm,type,
hoasapinj1_gthm: $o ).
thf(tp_hoasapinj1_lthm,type,
hoasapinj1_lthm: $o ).
thf(tp_hoasapinj2,type,
hoasapinj2: $o ).
thf(tp_hoasapinj2_gthm,type,
hoasapinj2_gthm: $o ).
thf(tp_hoasapinj2_lthm,type,
hoasapinj2_lthm: $o ).
thf(tp_hoasapnotvar,type,
hoasapnotvar: $o ).
thf(tp_hoasapnotvar_gthm,type,
hoasapnotvar_gthm: $o ).
thf(tp_hoasapnotvar_lthm,type,
hoasapnotvar_lthm: $o ).
thf(tp_hoasinduction,type,
hoasinduction: $o ).
thf(tp_hoasinduction_gthm,type,
hoasinduction_gthm: $o ).
thf(tp_hoasinduction_lem0,type,
hoasinduction_lem0: $o ).
thf(tp_hoasinduction_lem0_lthm,type,
hoasinduction_lem0_lthm: $o ).
thf(tp_hoasinduction_lem1,type,
hoasinduction_lem1: $o ).
thf(tp_hoasinduction_lem1_gthm,type,
hoasinduction_lem1_gthm: $o ).
thf(tp_hoasinduction_lem1_lthm,type,
hoasinduction_lem1_lthm: $o ).
thf(tp_hoasinduction_lem1v2,type,
hoasinduction_lem1v2: $o ).
thf(tp_hoasinduction_lem1v2_gthm,type,
hoasinduction_lem1v2_gthm: $o ).
thf(tp_hoasinduction_lem2,type,
hoasinduction_lem2: $o ).
thf(tp_hoasinduction_lem2_gthm,type,
hoasinduction_lem2_gthm: $o ).
thf(tp_hoasinduction_lem2_lthm,type,
hoasinduction_lem2_lthm: $o ).
thf(tp_hoasinduction_lem2v2,type,
hoasinduction_lem2v2: $o ).
thf(tp_hoasinduction_lem2v2_gthm,type,
hoasinduction_lem2v2_gthm: $o ).
thf(tp_hoasinduction_lem3,type,
hoasinduction_lem3: $o ).
thf(tp_hoasinduction_lem3_gthm,type,
hoasinduction_lem3_gthm: $o ).
thf(tp_hoasinduction_lem3_lthm,type,
hoasinduction_lem3_lthm: $o ).
thf(tp_hoasinduction_lem3a,type,
hoasinduction_lem3a: $o ).
thf(tp_hoasinduction_lem3a_gthm,type,
hoasinduction_lem3a_gthm: $o ).
thf(tp_hoasinduction_lem3a_lthm,type,
hoasinduction_lem3a_lthm: $o ).
thf(tp_hoasinduction_lem3aa,type,
hoasinduction_lem3aa: $o ).
thf(tp_hoasinduction_lem3aa_lthm,type,
hoasinduction_lem3aa_lthm: $o ).
thf(tp_hoasinduction_lem3aaa,type,
hoasinduction_lem3aaa: $o ).
thf(tp_hoasinduction_lem3b,type,
hoasinduction_lem3b: $o ).
thf(tp_hoasinduction_lem3b_gthm,type,
hoasinduction_lem3b_gthm: $o ).
thf(tp_hoasinduction_lem3b_lthm,type,
hoasinduction_lem3b_lthm: $o ).
thf(tp_hoasinduction_lem3v2,type,
hoasinduction_lem3v2: $o ).
thf(tp_hoasinduction_lem3v2_f,type,
hoasinduction_lem3v2_f: $o ).
thf(tp_hoasinduction_lem3v2_f_lthm,type,
hoasinduction_lem3v2_f_lthm: $o ).
thf(tp_hoasinduction_lem3v2_gthm,type,
hoasinduction_lem3v2_gthm: $o ).
thf(tp_hoasinduction_lem3v2_lthm,type,
hoasinduction_lem3v2_lthm: $o ).
thf(tp_hoasinduction_lem3v2a,type,
hoasinduction_lem3v2a: $o ).
thf(tp_hoasinduction_lem3v2a_lthm,type,
hoasinduction_lem3v2a_lthm: $o ).
thf(tp_hoasinduction_lthm,type,
hoasinduction_lthm: $o ).
thf(tp_hoasinduction_lthm_3,type,
hoasinduction_lthm_3: $o ).
thf(tp_hoasinduction_no_psi_cond,type,
hoasinduction_no_psi_cond: $o ).
thf(tp_hoasinduction_no_psi_cond_lthm,type,
hoasinduction_no_psi_cond_lthm: $o ).
thf(tp_hoasinduction_p_and_p_prime,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(tp_hoaslam,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(tp_hoaslaminj,type,
hoaslaminj: $o ).
thf(tp_hoaslaminj_gthm,type,
hoaslaminj_gthm: $o ).
thf(tp_hoaslaminj_lthm,type,
hoaslaminj_lthm: $o ).
thf(tp_hoaslamnotap,type,
hoaslamnotap: $o ).
thf(tp_hoaslamnotap_gthm,type,
hoaslamnotap_gthm: $o ).
thf(tp_hoaslamnotap_lthm,type,
hoaslamnotap_lthm: $o ).
thf(tp_hoaslamnotvar,type,
hoaslamnotvar: $o ).
thf(tp_hoaslamnotvar_gthm,type,
hoaslamnotvar_gthm: $o ).
thf(tp_hoaslamnotvar_lthm,type,
hoaslamnotvar_lthm: $o ).
thf(tp_hoasvar,type,
hoasvar: subst > term > subst > $o ).
thf(tp_id,type,
id: subst ).
thf(tp_induction,type,
induction: $o ).
thf(tp_induction2,type,
induction2: $o ).
thf(tp_induction2_gthm,type,
induction2_gthm: $o ).
thf(tp_induction2_lthm,type,
induction2_lthm: $o ).
thf(tp_induction2lem,type,
induction2lem: $o ).
thf(tp_induction2lem_gthm,type,
induction2lem_gthm: $o ).
thf(tp_induction2lem_lthm,type,
induction2lem_lthm: $o ).
thf(tp_lam,type,
lam: term > term ).
thf(tp_laminj,type,
laminj: $o ).
thf(tp_lamnotap,type,
lamnotap: $o ).
thf(tp_lamnotvar,type,
lamnotvar: $o ).
thf(tp_one,type,
one: term ).
thf(tp_push,type,
push: term > subst > subst ).
thf(tp_pushprop,type,
pushprop: $o ).
thf(tp_pushprop_gthm,type,
pushprop_gthm: $o ).
thf(tp_pushprop_lem0,type,
pushprop_lem0: $o ).
thf(tp_pushprop_lem0_gthm,type,
pushprop_lem0_gthm: $o ).
thf(tp_pushprop_lem0_lthm,type,
pushprop_lem0_lthm: $o ).
thf(tp_pushprop_lem1,type,
pushprop_lem1: $o ).
thf(tp_pushprop_lem1_gthm,type,
pushprop_lem1_gthm: $o ).
thf(tp_pushprop_lem1_lthm,type,
pushprop_lem1_lthm: $o ).
thf(tp_pushprop_lem1v2,type,
pushprop_lem1v2: $o ).
thf(tp_pushprop_lem1v2_gthm,type,
pushprop_lem1v2_gthm: $o ).
thf(tp_pushprop_lem1v2_lthm,type,
pushprop_lem1v2_lthm: $o ).
thf(tp_pushprop_lem2v2,type,
pushprop_lem2v2: $o ).
thf(tp_pushprop_lem2v2_gthm,type,
pushprop_lem2v2_gthm: $o ).
thf(tp_pushprop_lem2v2_lthm,type,
pushprop_lem2v2_lthm: $o ).
thf(tp_pushprop_lem3v2,type,
pushprop_lem3v2: $o ).
thf(tp_pushprop_lem3v2_lthm,type,
pushprop_lem3v2_lthm: $o ).
thf(tp_pushprop_lthm,type,
pushprop_lthm: $o ).
thf(tp_pushprop_lthm_orig,type,
pushprop_lthm_orig: $o ).
thf(tp_pushprop_p_and_p_prime,type,
pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
thf(tp_sK10_SY376,type,
sK10_SY376: ( subst > term > term ) > term ).
thf(tp_sK11_SY378,type,
sK11_SY378: ( subst > term > term ) > term ).
thf(tp_sK12_SY380,type,
sK12_SY380: ( term > $o ) > term ).
thf(tp_sK13_SY381,type,
sK13_SY381: ( subst > term > term ) > subst ).
thf(tp_sK14_SY382,type,
sK14_SY382: ( subst > term > term ) > subst ).
thf(tp_sK15_SY383,type,
sK15_SY383: ( subst > term > term ) > subst ).
thf(tp_sK16_SY331,type,
sK16_SY331: ( term > $o ) > term ).
thf(tp_sK17_SY370,type,
sK17_SY370: term > subst > ( term > $o ) > term ).
thf(tp_sK18_SY327,type,
sK18_SY327: ( term > $o ) > term ).
thf(tp_sK19_SY344,type,
sK19_SY344: ( term > $o ) > term ).
thf(tp_sK1_SY156,type,
sK1_SY156: term ).
thf(tp_sK20_SY327,type,
sK20_SY327: ( term > $o ) > term ).
thf(tp_sK21_SY390,type,
sK21_SY390: ( term > $o ) > term ).
thf(tp_sK22_SY344,type,
sK22_SY344: ( term > $o ) > term ).
thf(tp_sK23_SY391,type,
sK23_SY391: ( term > $o ) > term ).
thf(tp_sK24_SY385,type,
sK24_SY385: ( subst > term > term ) > ( subst > term > term ) > subst ).
thf(tp_sK25_SY314,type,
sK25_SY314: ( term > $o ) > term ).
thf(tp_sK26_SY314,type,
sK26_SY314: ( term > $o ) > term ).
thf(tp_sK27_SY392,type,
sK27_SY392: ( term > $o ) > term ).
thf(tp_sK28_SY393,type,
sK28_SY393: ( term > $o ) > term ).
thf(tp_sK29_SY394,type,
sK29_SY394: ( subst > term > term ) > ( subst > term > term ) > term ).
thf(tp_sK2_SY355,type,
sK2_SY355: term ).
thf(tp_sK30_SY314,type,
sK30_SY314: ( term > $o ) > term ).
thf(tp_sK31_SY398,type,
sK31_SY398: ( subst > term > term ) > ( subst > term > term ) > subst ).
thf(tp_sK32_SY329,type,
sK32_SY329: ( term > $o ) > term ).
thf(tp_sK33_SY329,type,
sK33_SY329: ( term > $o ) > term ).
thf(tp_sK34_SY346,type,
sK34_SY346: ( term > $o ) > term ).
thf(tp_sK35_SY346,type,
sK35_SY346: ( term > $o ) > term ).
thf(tp_sK36_SY329,type,
sK36_SY329: ( term > $o ) > term ).
thf(tp_sK37_SY329,type,
sK37_SY329: ( term > $o ) > term ).
thf(tp_sK38_SY329,type,
sK38_SY329: ( term > $o ) > term ).
thf(tp_sK39_SY346,type,
sK39_SY346: ( term > $o ) > term ).
thf(tp_sK3_SY292,type,
sK3_SY292: ( subst > term > term ) > subst ).
thf(tp_sK40_SY346,type,
sK40_SY346: ( term > $o ) > term ).
thf(tp_sK41_SY346,type,
sK41_SY346: ( term > $o ) > term ).
thf(tp_sK42_SY404,type,
sK42_SY404: term > subst > ( term > $o ) > term ).
thf(tp_sK43_SY407,type,
sK43_SY407: term > subst > ( term > $o ) > term ).
thf(tp_sK44_SY329,type,
sK44_SY329: ( term > $o ) > term ).
thf(tp_sK45_SY346,type,
sK45_SY346: ( term > $o ) > term ).
thf(tp_sK46_SY408,type,
sK46_SY408: term > subst > ( term > $o ) > term ).
thf(tp_sK47_SY420,type,
sK47_SY420: term > term > subst > ( term > $o ) > term ).
thf(tp_sK48_SY423,type,
sK48_SY423: term > term > subst > ( term > $o ) > term ).
thf(tp_sK49_SY424,type,
sK49_SY424: term > term > subst > ( term > $o ) > term ).
thf(tp_sK4_SY300,type,
sK4_SY300: ( subst > term > term ) > subst ).
thf(tp_sK5_SY303,type,
sK5_SY303: ( subst > term > term ) > subst ).
thf(tp_sK6_SY312,type,
sK6_SY312: ( term > $o ) > term ).
thf(tp_sK7_SY326,type,
sK7_SY326: ( term > $o ) > term ).
thf(tp_sK8_SY343,type,
sK8_SY343: ( term > $o ) > term ).
thf(tp_sK9_SY374,type,
sK9_SY374: ( subst > term > term ) > term ).
thf(tp_sh,type,
sh: subst ).
thf(tp_shinj,type,
shinj: $o ).
thf(tp_sub,type,
sub: term > subst > term ).
thf(tp_substmonoid,type,
substmonoid: $o ).
thf(tp_substmonoid_gthm,type,
substmonoid_gthm: $o ).
thf(tp_substmonoid_lthm,type,
substmonoid_lthm: $o ).
thf(tp_termmset,type,
termmset: $o ).
thf(tp_termmset_gthm,type,
termmset_gthm: $o ).
thf(tp_termmset_lthm,type,
termmset_lthm: $o ).
thf(tp_ulamvar1,type,
ulamvar1: $o ).
thf(tp_ulamvarind,type,
ulamvarind: $o ).
thf(tp_ulamvarsh,type,
ulamvarsh: $o ).
thf(tp_var,type,
var: term > $o ).
thf(apinj1,definition,
( apinj1
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apinj1) ).
thf(apinj2,definition,
( apinj2
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apinj2) ).
thf(apnotvar,definition,
( apnotvar
= ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apnotvar) ).
thf(axabs,definition,
( axabs
= ( ! [A: term,M: subst] :
( ( sub @ ( lam @ A ) @ M )
= ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axabs) ).
thf(axapp,definition,
( axapp
= ( ! [A: term,B: term,M: subst] :
( ( sub @ ( ap @ A @ B ) @ M )
= ( ap @ ( sub @ A @ M ) @ ( sub @ B @ M ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axapp) ).
thf(axassoc,definition,
( axassoc
= ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axassoc) ).
thf(axclos,definition,
( axclos
= ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axclos) ).
thf(axidl,definition,
( axidl
= ( ! [M: subst] :
( ( comp @ id @ M )
= M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axidl) ).
thf(axidr,definition,
( axidr
= ( ! [M: subst] :
( ( comp @ M @ id )
= M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axidr) ).
thf(axmap,definition,
( axmap
= ( ! [A: term,M: subst,N: subst] :
( ( comp @ ( push @ A @ M ) @ N )
= ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axmap) ).
thf(axscons,definition,
( axscons
= ( ! [M: subst] :
( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
= M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axscons) ).
thf(axshiftcons,definition,
( axshiftcons
= ( ! [A: term,M: subst] :
( ( comp @ sh @ ( push @ A @ M ) )
= M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axshiftcons) ).
thf(axvarcons,definition,
( axvarcons
= ( ! [A: term,M: subst] :
( ( sub @ one @ ( push @ A @ M ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axvarcons) ).
thf(axvarid,definition,
( axvarid
= ( ! [A: term] :
( ( sub @ A @ id )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axvarid) ).
thf(axvarshift,definition,
( axvarshift
= ( ( push @ one @ sh )
= id ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axvarshift) ).
thf(hoasap,definition,
( hoasap
= ( ^ [M: subst,A: term,N: subst,B: term] : ( ap @ ( sub @ A @ N ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasap) ).
thf(hoasapinj1,definition,
( hoasapinj1
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( hoasap @ id @ A @ id @ C )
= ( hoasap @ id @ B @ id @ D ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapinj1) ).
thf(hoasapinj1_gthm,definition,
( hoasapinj1_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> hoasapinj1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapinj1_gthm) ).
thf(hoasapinj1_lthm,definition,
( hoasapinj1_lthm
= ( axvarid
=> ( apinj1
=> hoasapinj1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapinj1_lthm) ).
thf(hoasapinj2,definition,
( hoasapinj2
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( hoasap @ id @ A @ id @ C )
= ( hoasap @ id @ B @ id @ D ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapinj2) ).
thf(hoasapinj2_gthm,definition,
( hoasapinj2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> hoasapinj2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapinj2_gthm) ).
thf(hoasapinj2_lthm,definition,
( hoasapinj2_lthm
= ( apinj2
=> hoasapinj2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapinj2_lthm) ).
thf(hoasapnotvar,definition,
( hoasapnotvar
= ( ! [A: term,B: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapnotvar) ).
thf(hoasapnotvar_gthm,definition,
( hoasapnotvar_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapnotvar_gthm) ).
thf(hoasapnotvar_lthm,definition,
( hoasapnotvar_lthm
= ( axvarid
=> ( apnotvar
=> hoasapnotvar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapnotvar_lthm) ).
thf(hoasinduction,definition,
( hoasinduction
= ( ! [P: subst > term > subst > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [A: term] :
( ( hoasvar @ id @ A @ id )
=> ( P @ id @ A @ id ) )
=> ( ! [A: term,B: term] :
( ( P @ id @ A @ id )
=> ( ( P @ id @ B @ id )
=> ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
=> ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ! [A: term] : ( P @ id @ A @ id ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction) ).
thf(hoasinduction_gthm,definition,
( hoasinduction_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> ( hoasinduction_lem3
=> hoasinduction ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_gthm) ).
thf(hoasinduction_lem0,definition,
( hoasinduction_lem0
= ( ! [P: subst > term > subst > $o] :
? [Q: term > $o] : ( hoasinduction_p_and_p_prime @ P @ Q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem0) ).
thf(hoasinduction_lem0_lthm,definition,
hoasinduction_lem0_lthm = hoasinduction_lem0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem0_lthm) ).
thf(hoasinduction_lem1,definition,
( hoasinduction_lem1
= ( ! [P: subst > term > subst > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [A: term] :
( ( hoasvar @ id @ A @ id )
=> ( P @ id @ A @ id ) )
=> ! [A: term] :
( ( var @ A )
=> ( P @ id @ A @ id ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem1) ).
thf(hoasinduction_lem1_gthm,definition,
( hoasinduction_lem1_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem1_gthm) ).
thf(hoasinduction_lem1_lthm,definition,
( hoasinduction_lem1_lthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem1_lthm) ).
thf(hoasinduction_lem1v2,definition,
( hoasinduction_lem1v2
= ( ! [P: subst > term > subst > $o,Q: term > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [A: term] :
( ( hoasvar @ id @ A @ id )
=> ( P @ id @ A @ id ) )
=> ( ( hoasinduction_p_and_p_prime @ P @ Q )
=> ! [A: term] :
( ( var @ A )
=> ( Q @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem1v2) ).
thf(hoasinduction_lem1v2_gthm,definition,
( hoasinduction_lem1v2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem1v2_gthm) ).
thf(hoasinduction_lem2,definition,
( hoasinduction_lem2
= ( ! [P: subst > term > subst > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [A: term,B: term] :
( ( P @ id @ A @ id )
=> ( ( P @ id @ B @ id )
=> ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
=> ! [A: term,B: term] :
( ( P @ id @ A @ id )
=> ( ( P @ id @ B @ id )
=> ( P @ id @ ( ap @ A @ B ) @ id ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem2) ).
thf(hoasinduction_lem2_gthm,definition,
( hoasinduction_lem2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem2_gthm) ).
thf(hoasinduction_lem2_lthm,definition,
( hoasinduction_lem2_lthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem2_lthm) ).
thf(hoasinduction_lem2v2,definition,
( hoasinduction_lem2v2
= ( ! [P: subst > term > subst > $o,Q: term > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [A: term,B: term] :
( ( P @ id @ A @ id )
=> ( ( P @ id @ B @ id )
=> ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ P @ Q )
=> ! [A: term,B: term] :
( ( Q @ A )
=> ( ( Q @ B )
=> ( Q @ ( ap @ A @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem2v2) ).
thf(hoasinduction_lem2v2_gthm,definition,
( hoasinduction_lem2v2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem2v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem2v2_gthm) ).
thf(hoasinduction_lem3,definition,
( hoasinduction_lem3
= ( ! [P: subst > term > subst > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ! [A: term] :
( ! [B: term] :
( ( P @ id @ B @ id )
=> ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
=> ( P @ id @ ( lam @ A ) @ id ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3) ).
thf(hoasinduction_lem3_gthm,definition,
( hoasinduction_lem3_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3_gthm) ).
thf(hoasinduction_lem3_lthm,definition,
( hoasinduction_lem3_lthm
= ( axvarid
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3_lthm) ).
thf(hoasinduction_lem3a,definition,
( hoasinduction_lem3a
= ( ! [P: subst > term > subst > $o] :
( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ! [A: term] :
( ! [B: term] :
( ( P @ id @ B @ id )
=> ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
=> ( P @ id @ ( lam @ A ) @ id ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3a) ).
thf(hoasinduction_lem3a_gthm,definition,
( hoasinduction_lem3a_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3a ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3a_gthm) ).
thf(hoasinduction_lem3a_lthm,definition,
( hoasinduction_lem3a_lthm
= ( axvarid
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3a_lthm) ).
thf(hoasinduction_lem3aa,definition,
( hoasinduction_lem3aa
= ( ! [P: subst > term > subst > $o] :
( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ! [A: term] :
( ! [B: term] :
( ( P @ id @ B @ id )
=> ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
=> ( P @ id @ ( lam @ ( sub @ A @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3aa) ).
thf(hoasinduction_lem3aa_lthm,definition,
( hoasinduction_lem3aa_lthm
= ( axclos
=> ( axmap
=> hoasinduction_lem3aa ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3aa_lthm) ).
thf(hoasinduction_lem3aaa,definition,
( hoasinduction_lem3aaa
= ( ! [P: subst > term > subst > $o] :
( ! [F: subst > term > term] :
( ? [C: term] :
! [M: subst,A: term,N: subst] :
( ( ( sub @ ( F @ M @ A ) @ N )
= ( sub @ ( sub @ C @ ( push @ A @ M ) ) @ N ) )
& ( ( sub @ C @ ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ! [A: term] :
( ! [B: term] :
( ( P @ id @ B @ id )
=> ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
=> ( P @ id @ ( lam @ ( sub @ A @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3aaa) ).
thf(hoasinduction_lem3b,definition,
( hoasinduction_lem3b
= ( ! [B: term] :
? [F: subst > term > term] :
( ( sub @ B @ ( push @ one @ sh ) )
= ( F @ sh @ one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3b) ).
thf(hoasinduction_lem3b_gthm,definition,
( hoasinduction_lem3b_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3b_gthm) ).
thf(hoasinduction_lem3b_lthm,definition,
hoasinduction_lem3b_lthm = hoasinduction_lem3b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3b_lthm) ).
thf(hoasinduction_lem3v2,definition,
( hoasinduction_lem3v2
= ( ! [P: subst > term > subst > $o,Q: term > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ P @ Q )
=> ! [A: term] :
( ! [B: term] :
( ( Q @ B )
=> ( Q @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( Q @ ( lam @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3v2) ).
thf(hoasinduction_lem3v2_f,definition,
( hoasinduction_lem3v2_f
= ( ! [B: term] :
? [F: subst > term > term] :
! [A: term,M: subst] :
( ( F @ M @ A )
= ( sub @ B @ ( push @ A @ M ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3v2_f) ).
thf(hoasinduction_lem3v2_f_lthm,definition,
hoasinduction_lem3v2_f_lthm = hoasinduction_lem3v2_f,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3v2_f_lthm) ).
thf(hoasinduction_lem3v2_gthm,definition,
( hoasinduction_lem3v2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem3v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3v2_gthm) ).
thf(hoasinduction_lem3v2_lthm,definition,
( hoasinduction_lem3v2_lthm
= ( axvarid
=> ( axvarshift
=> ( axclos
=> ( axmap
=> hoasinduction_lem3v2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3v2_lthm) ).
thf(hoasinduction_lem3v2a,definition,
( hoasinduction_lem3v2a
= ( ! [P: subst > term > subst > $o,Q: term > $o] :
( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ P @ Q )
=> ! [A: term] :
( ! [B: term] :
( ( Q @ B )
=> ( Q @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( Q @ ( lam @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3v2a) ).
thf(hoasinduction_lem3v2a_lthm,definition,
( hoasinduction_lem3v2a_lthm
= ( hoasinduction_lem3v2_f
=> ( axvarid
=> ( axvarshift
=> ( axclos
=> ( axmap
=> hoasinduction_lem3v2a ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3v2a_lthm) ).
thf(hoasinduction_lthm,definition,
( hoasinduction_lthm
= ( induction2
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> ( hoasinduction_lem3
=> hoasinduction ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lthm) ).
thf(hoasinduction_lthm_3,definition,
( hoasinduction_lthm_3
= ( hoasinduction_lem0
=> ( induction2
=> ( axvarid
=> ( hoasinduction_lem3v2a
=> hoasinduction ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lthm_3) ).
thf(hoasinduction_no_psi_cond,definition,
( hoasinduction_no_psi_cond
= ( ! [P: subst > term > subst > $o] :
( ! [A: term,B: term] :
( ( P @ id @ A @ id )
=> ( ( P @ id @ B @ id )
=> ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
=> ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ! [A: term] : ( P @ id @ A @ id ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_no_psi_cond) ).
thf(hoasinduction_no_psi_cond_lthm,definition,
( hoasinduction_no_psi_cond_lthm
= ( hoasinduction_lem0
=> ( induction2
=> ( axvarid
=> ( hoasinduction_lem3v2a
=> hoasinduction_no_psi_cond ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_no_psi_cond_lthm) ).
thf(hoasinduction_p_and_p_prime,definition,
( hoasinduction_p_and_p_prime
= ( ^ [P: subst > term > subst > $o,Q: term > $o] :
! [X: term] :
( ( Q @ X )
<=> ( P @ id @ X @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_p_and_p_prime) ).
thf(hoaslam,definition,
( hoaslam
= ( ^ [M: subst,F: subst > term > term] : ( lam @ ( F @ sh @ one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslam) ).
thf(hoaslaminj,definition,
( hoaslaminj
= ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [G: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( G @ M @ A ) @ N )
= ( G @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ( ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
= ( hoaslam @ id
@ ^ [M: subst,A: term] : ( G @ M @ A ) ) )
=> ! [M: subst,A: term] :
( ( F @ M @ A )
= ( G @ M @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslaminj) ).
thf(hoaslaminj_gthm,definition,
( hoaslaminj_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> hoaslaminj ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslaminj_gthm) ).
thf(hoaslaminj_lthm,definition,
( hoaslaminj_lthm
= ( axvarcons
=> ( axshiftcons
=> ( laminj
=> hoaslaminj ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslaminj_lthm) ).
thf(hoaslamnotap,definition,
( hoaslamnotap
= ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [A: term,B: term] :
( ( hoaslam @ id
@ ^ [M: subst,C: term] : ( F @ M @ C ) )
!= ( hoasap @ id @ A @ id @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslamnotap) ).
thf(hoaslamnotap_gthm,definition,
( hoaslamnotap_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslamnotap_gthm) ).
thf(hoaslamnotap_lthm,definition,
( hoaslamnotap_lthm
= ( lamnotap
=> hoaslamnotap ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslamnotap_lthm) ).
thf(hoaslamnotvar,definition,
( hoaslamnotvar
= ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslamnotvar) ).
thf(hoaslamnotvar_gthm,definition,
( hoaslamnotvar_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslamnotvar_gthm) ).
thf(hoaslamnotvar_lthm,definition,
( hoaslamnotvar_lthm
= ( axvarid
=> ( lamnotvar
=> hoaslamnotvar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslamnotvar_lthm) ).
thf(hoasvar,definition,
( hoasvar
= ( ^ [M: subst,A: term,N: subst] : ( var @ ( sub @ A @ N ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasvar) ).
thf(induction,definition,
( induction
= ( ! [P: term > $o] :
( ! [A: term] :
( ( var @ A )
=> ( P @ A ) )
=> ( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ( P @ A )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term] : ( P @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction) ).
thf(induction2,definition,
( induction2
= ( ! [P: term > $o] :
( ! [A: term] :
( ( var @ A )
=> ( P @ A ) )
=> ( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ! [B: term] :
( ( P @ B )
=> ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term] : ( P @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction2) ).
thf(induction2_gthm,definition,
( induction2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> induction2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction2_gthm) ).
thf(induction2_lthm,definition,
( induction2_lthm
= ( axvarid
=> ( induction2lem
=> induction2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction2_lthm) ).
thf(induction2lem,definition,
( induction2lem
= ( ! [P: term > $o] :
( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ! [B: term] :
( ( P @ B )
=> ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term,M: subst] :
( ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ M ) ) )
=> ( P @ ( sub @ A @ M ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction2lem) ).
thf(induction2lem_gthm,definition,
( induction2lem_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> induction2lem ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction2lem_gthm) ).
thf(induction2lem_lthm,definition,
( induction2lem_lthm
= ( axapp
=> ( axvarcons
=> ( axabs
=> ( axclos
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( induction
=> ( pushprop
=> induction2lem ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction2lem_lthm) ).
thf(laminj,definition,
( laminj
= ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',laminj) ).
thf(lamnotap,definition,
( lamnotap
= ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamnotap) ).
thf(lamnotvar,definition,
( lamnotvar
= ( ! [A: term] :
~ ( var @ ( lam @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamnotvar) ).
thf(pushprop,definition,
( pushprop
= ( ! [P: term > $o,A: term,M: subst] :
( ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ M ) ) )
=> ( ( P @ A )
=> ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop) ).
thf(pushprop_gthm,definition,
( pushprop_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> pushprop ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_gthm) ).
thf(pushprop_lem0,definition,
( pushprop_lem0
= ( ! [P: term > $o,A: term,M: subst] :
? [Q: term > $o] : ( pushprop_p_and_p_prime @ A @ M @ P @ Q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem0) ).
thf(pushprop_lem0_gthm,definition,
( pushprop_lem0_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> pushprop_lem0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem0_gthm) ).
thf(pushprop_lem0_lthm,definition,
pushprop_lem0_lthm = pushprop_lem0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem0_lthm) ).
thf(pushprop_lem1,definition,
( pushprop_lem1
= ( ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
( ( P @ A )
=> ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem1) ).
thf(pushprop_lem1_gthm,definition,
( pushprop_lem1_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> pushprop_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem1_gthm) ).
thf(pushprop_lem1_lthm,definition,
( pushprop_lem1_lthm
= ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop_lem1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem1_lthm) ).
thf(pushprop_lem1v2,definition,
( pushprop_lem1v2
= ( ! [P: term > $o,Q: term > $o,A: term,M: subst] :
( ( P @ A )
=> ( ( pushprop_p_and_p_prime @ A @ M @ P @ Q )
=> ( Q @ one ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem1v2) ).
thf(pushprop_lem1v2_gthm,definition,
( pushprop_lem1v2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> pushprop_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem1v2_gthm) ).
thf(pushprop_lem1v2_lthm,definition,
( pushprop_lem1v2_lthm
= ( axvarcons
=> pushprop_lem1v2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem1v2_lthm) ).
thf(pushprop_lem2v2,definition,
( pushprop_lem2v2
= ( ! [P: term > $o,Q: term > $o,A: term,M: subst] :
( ( pushprop_p_and_p_prime @ A @ M @ P @ Q )
=> ( ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ M ) ) )
=> ! [C: term] :
( ( var @ C )
=> ( ( Q @ C )
=> ( Q @ ( sub @ C @ sh ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem2v2) ).
thf(pushprop_lem2v2_gthm,definition,
( pushprop_lem2v2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> pushprop_lem2v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem2v2_gthm) ).
thf(pushprop_lem2v2_lthm,definition,
( pushprop_lem2v2_lthm
= ( axclos
=> ( axshiftcons
=> pushprop_lem2v2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem2v2_lthm) ).
thf(pushprop_lem3v2,definition,
( pushprop_lem3v2
= ( ! [P: term > $o,Q: term > $o,A: term,M: subst] :
( ( pushprop_p_and_p_prime @ A @ M @ P @ Q )
=> ( ! [B: term] :
( ( var @ B )
=> ( Q @ B ) )
=> ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem3v2) ).
thf(pushprop_lem3v2_lthm,definition,
pushprop_lem3v2_lthm = pushprop_lem3v2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem3v2_lthm) ).
thf(pushprop_lthm,definition,
( pushprop_lthm
= ( pushprop_lem0
=> ( ulamvar1
=> ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lthm) ).
thf(pushprop_lthm_orig,definition,
( pushprop_lthm_orig
= ( ulamvar1
=> ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lthm_orig) ).
thf(pushprop_p_and_p_prime,definition,
( pushprop_p_and_p_prime
= ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
! [X: term] :
( ( Q @ X )
<=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_p_and_p_prime) ).
thf(shinj,definition,
( shinj
= ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
= ( sub @ B @ sh ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',shinj) ).
thf(substmonoid,definition,
( substmonoid
= ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) )
& ! [M: subst] :
( ( comp @ id @ M )
= M )
& ! [M: subst] :
( ( comp @ M @ id )
= M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substmonoid) ).
thf(substmonoid_gthm,definition,
( substmonoid_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> substmonoid ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substmonoid_gthm) ).
thf(substmonoid_lthm,definition,
( substmonoid_lthm
= ( axidl
=> ( axassoc
=> ( axidr
=> substmonoid ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substmonoid_lthm) ).
thf(termmset,definition,
( termmset
= ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) )
& ! [A: term] :
( ( sub @ A @ id )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',termmset) ).
thf(termmset_gthm,definition,
( termmset_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> termmset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',termmset_gthm) ).
thf(termmset_lthm,definition,
( termmset_lthm
= ( axvarid
=> ( axclos
=> termmset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',termmset_lthm) ).
thf(ulamvar1,definition,
( ulamvar1
= ( var @ one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ulamvar1) ).
thf(ulamvarind,definition,
( ulamvarind
= ( ! [P: term > $o] :
( ( P @ one )
=> ( ! [A: term] :
( ( var @ A )
=> ( ( P @ A )
=> ( P @ ( sub @ A @ sh ) ) ) )
=> ! [A: term] :
( ( var @ A )
=> ( P @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ulamvarind) ).
thf(ulamvarsh,definition,
( ulamvarsh
= ( ! [A: term] :
( ( var @ A )
=> ( var @ ( sub @ A @ sh ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ulamvarsh) ).
thf(1,conjecture,
hoasapnotvar_gthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
hoasapnotvar_gthm = $false,
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: term,B: term,M: subst] :
( ( sub @ ( ap @ A @ B ) @ M )
= ( ap @ ( sub @ A @ M ) @ ( sub @ B @ M ) ) )
=> ( ! [A: term,M: subst] :
( ( sub @ one @ ( push @ A @ M ) )
= A )
=> ( ! [A: term] :
( ( sub @ A @ id )
= A )
=> ( ! [A: term,M: subst] :
( ( sub @ ( lam @ A ) @ M )
= ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) )
=> ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) )
=> ( ! [M: subst] :
( ( comp @ id @ M )
= M )
=> ( ! [A: term,M: subst] :
( ( comp @ sh @ ( push @ A @ M ) )
= M )
=> ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) )
=> ( ! [A: term,M: subst,N: subst] :
( ( comp @ ( push @ A @ M ) @ N )
= ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) )
=> ( ! [M: subst] :
( ( comp @ M @ id )
= M )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [M: subst] :
( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
= M )
=> ( ( var @ one )
=> ( ! [A: term] :
( ( var @ A )
=> ( var @ ( sub @ A @ sh ) ) )
=> ( ! [P: term > $o] :
( ( P @ one )
=> ( ! [A: term] :
( ( var @ A )
=> ( ( P @ A )
=> ( P @ ( sub @ A @ sh ) ) ) )
=> ! [A: term] :
( ( var @ A )
=> ( P @ A ) ) ) )
=> ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( A = B ) )
=> ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( C = D ) )
=> ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) )
=> ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
= ( sub @ B @ sh ) )
=> ( A = B ) )
=> ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) )
=> ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) )
=> ( ! [A: term] :
~ ( var @ ( lam @ A ) )
=> ( ! [P: term > $o] :
( ! [A: term] :
( ( var @ A )
=> ( P @ A ) )
=> ( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ( P @ A )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term] : ( P @ A ) ) ) )
=> ( ! [P: term > $o,A: term,M: subst] :
( ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ M ) ) )
=> ( ( P @ A )
=> ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) )
=> ( ! [P: term > $o] :
( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ! [B: term] :
( ( P @ B )
=> ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term,M: subst] :
( ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ M ) ) )
=> ( P @ ( sub @ A @ M ) ) ) ) )
=> ( ! [P: term > $o] :
( ! [A: term] :
( ( var @ A )
=> ( P @ A ) )
=> ( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ! [B: term] :
( ( P @ B )
=> ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term] : ( P @ A ) ) ) )
=> ( ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) )
& ! [M: subst] :
( ( comp @ id @ M )
= M )
& ! [M: subst] :
( ( comp @ M @ id )
= M ) )
=> ( ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) )
& ! [A: term] :
( ( sub @ A @ id )
= A ) )
=> ( ! [SY79: term,SY80: term,SY81: term,SY82: term] :
( ( ( ap @ ( sub @ SY79 @ id ) @ SY81 )
= ( ap @ ( sub @ SY80 @ id ) @ SY82 ) )
=> ( SY79 = SY80 ) )
=> ( ! [SY95: term,SY96: term,SY97: term,SY98: term] :
( ( ( ap @ ( sub @ SY95 @ id ) @ SY97 )
= ( ap @ ( sub @ SY96 @ id ) @ SY98 ) )
=> ( SY97 = SY98 ) )
=> ( ! [SY111: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY111 @ M @ A ) @ N )
= ( SY111 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [SY115: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY115 @ M @ A ) @ N )
= ( SY115 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ( ( lam @ ( SY111 @ sh @ one ) )
= ( lam @ ( SY115 @ sh @ one ) ) )
=> ! [M: subst,A: term] :
( ( SY111 @ M @ A )
= ( SY115 @ M @ A ) ) ) ) )
=> ( ! [SY129: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY129 @ M @ A ) @ N )
= ( SY129 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [SY133: term,SY134: term] :
( ( lam @ ( SY129 @ sh @ one ) )
!= ( ap @ ( sub @ SY133 @ id ) @ SY134 ) ) )
=> ( ! [SY145: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY145 @ M @ A ) @ N )
= ( SY145 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( SY145 @ sh @ one ) ) @ id ) ) )
=> ! [SY156: term,SY157: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SY156 @ id ) @ SY157 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(4,plain,
( ( ! [A: term,B: term,M: subst] :
( ( sub @ ( ap @ A @ B ) @ M )
= ( ap @ ( sub @ A @ M ) @ ( sub @ B @ M ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: term,M: subst] :
( ( sub @ one @ ( push @ A @ M ) )
= A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: term] :
( ( sub @ A @ id )
= A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [A: term,M: subst] :
( ( sub @ ( lam @ A ) @ M )
= ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( ! [M: subst] :
( ( comp @ id @ M )
= M ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(10,plain,
( ( ! [A: term,M: subst] :
( ( comp @ sh @ ( push @ A @ M ) )
= M ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(11,plain,
( ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [A: term,M: subst,N: subst] :
( ( comp @ ( push @ A @ M ) @ N )
= ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [M: subst] :
( ( comp @ M @ id )
= M ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(14,plain,
( ( ( push @ one @ sh )
= id )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [M: subst] :
( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
= M ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(16,plain,
( ( var @ one )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [A: term] :
( ( var @ A )
=> ( var @ ( sub @ A @ sh ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [P: term > $o] :
( ( P @ one )
=> ( ! [A: term] :
( ( var @ A )
=> ( ( P @ A )
=> ( P @ ( sub @ A @ sh ) ) ) )
=> ! [A: term] :
( ( var @ A )
=> ( P @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(19,plain,
( ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( A = B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( C = D ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(21,plain,
( ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(22,plain,
( ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
= ( sub @ B @ sh ) )
=> ( A = B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(23,plain,
( ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(24,plain,
( ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(25,plain,
( ( ! [A: term] :
~ ( var @ ( lam @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(26,plain,
( ( ! [P: term > $o] :
( ! [A: term] :
( ( var @ A )
=> ( P @ A ) )
=> ( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ( P @ A )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term] : ( P @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(27,plain,
( ( ! [P: term > $o,A: term,M: subst] :
( ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ M ) ) )
=> ( ( P @ A )
=> ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(28,plain,
( ( ! [P: term > $o] :
( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ! [B: term] :
( ( P @ B )
=> ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term,M: subst] :
( ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ M ) ) )
=> ( P @ ( sub @ A @ M ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(29,plain,
( ( ! [P: term > $o] :
( ! [A: term] :
( ( var @ A )
=> ( P @ A ) )
=> ( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ! [B: term] :
( ( P @ B )
=> ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term] : ( P @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(30,plain,
( ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(31,plain,
( ( ! [M: subst] :
( ( comp @ id @ M )
= M ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(32,plain,
( ( ! [M: subst] :
( ( comp @ M @ id )
= M ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(33,plain,
( ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(34,plain,
( ( ! [A: term] :
( ( sub @ A @ id )
= A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(35,plain,
( ( ! [SY79: term,SY80: term,SY81: term,SY82: term] :
( ( ( ap @ ( sub @ SY79 @ id ) @ SY81 )
= ( ap @ ( sub @ SY80 @ id ) @ SY82 ) )
=> ( SY79 = SY80 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(36,plain,
( ( ! [SY95: term,SY96: term,SY97: term,SY98: term] :
( ( ( ap @ ( sub @ SY95 @ id ) @ SY97 )
= ( ap @ ( sub @ SY96 @ id ) @ SY98 ) )
=> ( SY97 = SY98 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(37,plain,
( ( ! [SY111: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY111 @ M @ A ) @ N )
= ( SY111 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [SY115: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY115 @ M @ A ) @ N )
= ( SY115 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ( ( lam @ ( SY111 @ sh @ one ) )
= ( lam @ ( SY115 @ sh @ one ) ) )
=> ! [M: subst,A: term] :
( ( SY111 @ M @ A )
= ( SY115 @ M @ A ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(38,plain,
( ( ! [SY129: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY129 @ M @ A ) @ N )
= ( SY129 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [SY133: term,SY134: term] :
( ( lam @ ( SY129 @ sh @ one ) )
!= ( ap @ ( sub @ SY133 @ id ) @ SY134 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(39,plain,
( ( ! [SY145: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY145 @ M @ A ) @ N )
= ( SY145 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( SY145 @ sh @ one ) ) @ id ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(40,plain,
( ( ! [SY156: term,SY157: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SY156 @ id ) @ SY157 ) @ id ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(41,plain,
( ( ~ ! [SY156: term,SY157: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SY156 @ id ) @ SY157 ) @ id ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[40]) ).
thf(42,plain,
( ( ! [SY145: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY145 @ M @ A ) @ N )
= ( SY145 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( SY145 @ sh @ one ) ) @ id ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(43,plain,
( ( ! [SY129: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY129 @ M @ A ) @ N )
= ( SY129 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [SY133: term,SY134: term] :
( ( lam @ ( SY129 @ sh @ one ) )
!= ( ap @ ( sub @ SY133 @ id ) @ SY134 ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(44,plain,
( ( ! [SY111: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY111 @ M @ A ) @ N )
= ( SY111 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [SY115: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY115 @ M @ A ) @ N )
= ( SY115 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ( ( lam @ ( SY111 @ sh @ one ) )
= ( lam @ ( SY115 @ sh @ one ) ) )
=> ! [M: subst,A: term] :
( ( SY111 @ M @ A )
= ( SY115 @ M @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(45,plain,
( ( ! [SY95: term,SY96: term,SY97: term,SY98: term] :
( ( ( ap @ ( sub @ SY95 @ id ) @ SY97 )
= ( ap @ ( sub @ SY96 @ id ) @ SY98 ) )
=> ( SY97 = SY98 ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(46,plain,
( ( ! [SY79: term,SY80: term,SY81: term,SY82: term] :
( ( ( ap @ ( sub @ SY79 @ id ) @ SY81 )
= ( ap @ ( sub @ SY80 @ id ) @ SY82 ) )
=> ( SY79 = SY80 ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(47,plain,
( ( ! [A: term] :
( ( sub @ A @ id )
= A ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(48,plain,
( ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(49,plain,
( ( ! [M: subst] :
( ( comp @ M @ id )
= M ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(50,plain,
( ( ! [M: subst] :
( ( comp @ id @ M )
= M ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(51,plain,
( ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(52,plain,
( ( ! [P: term > $o] :
( ! [A: term] :
( ( var @ A )
=> ( P @ A ) )
=> ( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ! [B: term] :
( ( P @ B )
=> ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term] : ( P @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(53,plain,
( ( ! [P: term > $o] :
( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ! [B: term] :
( ( P @ B )
=> ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term,M: subst] :
( ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ M ) ) )
=> ( P @ ( sub @ A @ M ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(54,plain,
( ( ! [P: term > $o,A: term,M: subst] :
( ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ M ) ) )
=> ( ( P @ A )
=> ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(55,plain,
( ( ! [P: term > $o] :
( ! [A: term] :
( ( var @ A )
=> ( P @ A ) )
=> ( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ( P @ A )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term] : ( P @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(56,plain,
( ( ! [A: term] :
~ ( var @ ( lam @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(57,plain,
( ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(58,plain,
( ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(59,plain,
( ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
= ( sub @ B @ sh ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(60,plain,
( ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(61,plain,
( ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( C = D ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(62,plain,
( ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(63,plain,
( ( ! [P: term > $o] :
( ( P @ one )
=> ( ! [A: term] :
( ( var @ A )
=> ( ( P @ A )
=> ( P @ ( sub @ A @ sh ) ) ) )
=> ! [A: term] :
( ( var @ A )
=> ( P @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(64,plain,
( ( ! [A: term] :
( ( var @ A )
=> ( var @ ( sub @ A @ sh ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(65,plain,
( ( var @ one )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(66,plain,
( ( ! [M: subst] :
( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
= M ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(67,plain,
( ( ( push @ one @ sh )
= id )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(68,plain,
( ( ! [M: subst] :
( ( comp @ M @ id )
= M ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(69,plain,
( ( ! [A: term,M: subst,N: subst] :
( ( comp @ ( push @ A @ M ) @ N )
= ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(70,plain,
( ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(71,plain,
( ( ! [A: term,M: subst] :
( ( comp @ sh @ ( push @ A @ M ) )
= M ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(72,plain,
( ( ! [M: subst] :
( ( comp @ id @ M )
= M ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(73,plain,
( ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(74,plain,
( ( ! [A: term,M: subst] :
( ( sub @ ( lam @ A ) @ M )
= ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(75,plain,
( ( ! [A: term] :
( ( sub @ A @ id )
= A ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(76,plain,
( ( ! [A: term,M: subst] :
( ( sub @ one @ ( push @ A @ M ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(77,plain,
( ( ! [A: term,B: term,M: subst] :
( ( sub @ ( ap @ A @ B ) @ M )
= ( ap @ ( sub @ A @ M ) @ ( sub @ B @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(78,plain,
( ( ~ ! [SY156: term,SY157: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SY156 @ id ) @ SY157 ) @ id ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(79,plain,
( ( ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(80,plain,
( ( ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(81,plain,
( ( ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(82,plain,
( ( ! [SX0: term] :
( ~ ( var @ SX0 )
| ( var @ ( sub @ SX0 @ sh ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(83,plain,
( ( ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(84,plain,
( ( ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(85,plain,
( ( ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(86,plain,
( ( ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(87,plain,
( ( ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(88,plain,
( ( ! [SX0: term,SX1: term] :
( ( ( lam @ SX0 )
!= ( lam @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(89,plain,
( ( ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(90,plain,
( ( ! [SX0: term > $o] :
( ~ ( SX0 @ one )
| ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ~ ( SX0 @ SX1 )
| ( SX0 @ ( sub @ SX1 @ sh ) ) )
| ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(91,plain,
( ( ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(92,plain,
( ( ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(93,plain,
( ( ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(94,plain,
( ( ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(95,plain,
! [SV1: term] :
( ( ( sub @ SV1 @ id )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(96,plain,
! [SV2: term] :
( ( ! [SY276: subst,SY277: subst] :
( ( sub @ ( sub @ SV2 @ SY276 ) @ SY277 )
= ( sub @ SV2 @ ( comp @ SY276 @ SY277 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(97,plain,
! [SV3: subst] :
( ( ( comp @ SV3 @ id )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(98,plain,
! [SV4: subst] :
( ( ( comp @ id @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(99,plain,
! [SV5: subst] :
( ( ! [SY278: subst,SY279: subst] :
( ( comp @ ( comp @ SV5 @ SY278 ) @ SY279 )
= ( comp @ SV5 @ ( comp @ SY278 @ SY279 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(100,plain,
! [SV6: term] :
( ( ~ ( var @ ( lam @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(101,plain,
! [SV7: term] :
( ( ! [SY280: term] :
~ ( var @ ( ap @ SV7 @ SY280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(102,plain,
! [SV8: subst] :
( ( ( push @ ( sub @ one @ SV8 ) @ ( comp @ sh @ SV8 ) )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(103,plain,
! [SV9: subst] :
( ( ( comp @ SV9 @ id )
= SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(104,plain,
! [SV10: term] :
( ( ! [SY281: subst,SY282: subst] :
( ( comp @ ( push @ SV10 @ SY281 ) @ SY282 )
= ( push @ ( sub @ SV10 @ SY282 ) @ ( comp @ SY281 @ SY282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(105,plain,
! [SV11: subst] :
( ( ! [SY283: subst,SY284: subst] :
( ( comp @ ( comp @ SV11 @ SY283 ) @ SY284 )
= ( comp @ SV11 @ ( comp @ SY283 @ SY284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(106,plain,
! [SV12: term] :
( ( ! [SY285: subst] :
( ( comp @ sh @ ( push @ SV12 @ SY285 ) )
= SY285 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(107,plain,
! [SV13: subst] :
( ( ( comp @ id @ SV13 )
= SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(108,plain,
! [SV14: term] :
( ( ! [SY286: subst,SY287: subst] :
( ( sub @ ( sub @ SV14 @ SY286 ) @ SY287 )
= ( sub @ SV14 @ ( comp @ SY286 @ SY287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(109,plain,
! [SV15: term] :
( ( ! [SY288: subst] :
( ( sub @ ( lam @ SV15 ) @ SY288 )
= ( lam @ ( sub @ SV15 @ ( push @ one @ ( comp @ SY288 @ sh ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(110,plain,
! [SV16: term] :
( ( ( sub @ SV16 @ id )
= SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(111,plain,
! [SV17: term] :
( ( ! [SY289: subst] :
( ( sub @ one @ ( push @ SV17 @ SY289 ) )
= SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(112,plain,
! [SV18: term] :
( ( ! [SY290: term,SY291: subst] :
( ( sub @ ( ap @ SV18 @ SY290 ) @ SY291 )
= ( ap @ ( sub @ SV18 @ SY291 ) @ ( sub @ SY290 @ SY291 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(113,plain,
( ( ! [SY156: term,SY157: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SY156 @ id ) @ SY157 ) @ id ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(114,plain,
! [SV19: subst > term > term] :
( ( ~ ! [SY292: subst,SY293: term,SY294: subst] :
( ( sub @ ( SV19 @ SY292 @ SY293 ) @ SY294 )
= ( SV19 @ ( comp @ SY292 @ SY294 ) @ ( sub @ SY293 @ SY294 ) ) )
| ! [SY295: term,SY296: term] :
( ( lam @ ( SV19 @ sh @ one ) )
!= ( ap @ ( sub @ SY295 @ id ) @ SY296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(115,plain,
! [SV20: term] :
( ( ! [SY297: term,SY298: term,SY299: term] :
( ( ( ap @ ( sub @ SV20 @ id ) @ SY298 )
!= ( ap @ ( sub @ SY297 @ id ) @ SY299 ) )
| ( SV20 = SY297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(116,plain,
! [SV21: subst > term > term] :
( ( ~ ! [SY300: subst,SY301: term,SY302: subst] :
( ( sub @ ( SV21 @ SY300 @ SY301 ) @ SY302 )
= ( SV21 @ ( comp @ SY300 @ SY302 ) @ ( sub @ SY301 @ SY302 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SV21 @ sh @ one ) ) @ id ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(117,plain,
! [SV22: term] :
( ( ~ ( var @ SV22 )
| ( var @ ( sub @ SV22 @ sh ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(118,plain,
! [SV23: subst > term > term] :
( ( ~ ! [SY303: subst,SY304: term,SY305: subst] :
( ( sub @ ( SV23 @ SY303 @ SY304 ) @ SY305 )
= ( SV23 @ ( comp @ SY303 @ SY305 ) @ ( sub @ SY304 @ SY305 ) ) )
| ! [SY306: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SY306 @ SX2 @ SX3 ) @ SX4 )
= ( SY306 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SV23 @ sh @ one ) )
!= ( lam @ ( SY306 @ sh @ one ) ) )
| ! [SY310: subst,SY311: term] :
( ( SV23 @ SY310 @ SY311 )
= ( SY306 @ SY310 @ SY311 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(119,plain,
! [SV24: term > $o] :
( ( ~ ! [SY312: term,SY313: term] :
( ~ ( SV24 @ SY312 )
| ~ ( SV24 @ SY313 )
| ( SV24 @ ( ap @ SY312 @ SY313 ) ) )
| ~ ! [SY314: term] :
( ~ ! [SY315: term] :
( ~ ( SV24 @ SY315 )
| ( SV24 @ ( sub @ SY314 @ ( push @ SY315 @ id ) ) ) )
| ( SV24 @ ( lam @ SY314 ) ) )
| ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(120,plain,
! [SV25: term] :
( ( ! [SY319: term,SY320: term] :
( ( lam @ SV25 )
!= ( ap @ SY319 @ SY320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(121,plain,
! [SV26: term] :
( ( ! [SY321: term,SY322: term,SY323: term] :
( ( ( ap @ SV26 @ SY322 )
!= ( ap @ SY321 @ SY323 ) )
| ( SY322 = SY323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(122,plain,
! [SV27: term] :
( ( ! [SY324: term] :
( ( ( sub @ SV27 @ sh )
!= ( sub @ SY324 @ sh ) )
| ( SV27 = SY324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(123,plain,
! [SV28: term] :
( ( ! [SY325: term] :
( ( ( lam @ SV28 )
!= ( lam @ SY325 ) )
| ( SV28 = SY325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(124,plain,
! [SV29: term > $o] :
( ( ~ ! [SY326: term] :
( ~ ( var @ SY326 )
| ( SV29 @ SY326 ) )
| ~ ! [SY327: term,SY328: term] :
( ~ ( SV29 @ SY327 )
| ~ ( SV29 @ SY328 )
| ( SV29 @ ( ap @ SY327 @ SY328 ) ) )
| ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(125,plain,
! [SV30: term > $o] :
( ( ~ ( SV30 @ one )
| ~ ! [SY331: term] :
( ~ ( var @ SY331 )
| ~ ( SV30 @ SY331 )
| ( SV30 @ ( sub @ SY331 @ sh ) ) )
| ! [SY332: term] :
( ~ ( var @ SY332 )
| ( SV30 @ SY332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(126,plain,
! [SV31: term > $o] :
( ( ! [SY333: term,SY334: subst] :
( ~ ! [SY335: term] :
( ~ ( var @ SY335 )
| ( SV31 @ ( sub @ SY335 @ SY334 ) ) )
| ~ ( SV31 @ SY333 )
| ! [SY336: term] :
( ~ ( var @ SY336 )
| ( SV31 @ ( sub @ SY336 @ ( push @ SY333 @ SY334 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(127,plain,
! [SV32: term] :
( ( ! [SY337: term,SY338: term,SY339: term] :
( ( ( ap @ ( sub @ SV32 @ id ) @ SY338 )
!= ( ap @ ( sub @ SY337 @ id ) @ SY339 ) )
| ( SY338 = SY339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(128,plain,
! [SV33: term] :
( ( ! [SY340: term,SY341: term,SY342: term] :
( ( ( ap @ SV33 @ SY341 )
!= ( ap @ SY340 @ SY342 ) )
| ( SV33 = SY340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(129,plain,
! [SV34: term > $o] :
( ( ~ ! [SY343: term] :
( ~ ( var @ SY343 )
| ( SV34 @ SY343 ) )
| ~ ! [SY344: term,SY345: term] :
( ~ ( SV34 @ SY344 )
| ~ ( SV34 @ SY345 )
| ( SV34 @ ( ap @ SY344 @ SY345 ) ) )
| ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(130,plain,
! [SV35: subst,SV2: term] :
( ( ! [SY349: subst] :
( ( sub @ ( sub @ SV2 @ SV35 ) @ SY349 )
= ( sub @ SV2 @ ( comp @ SV35 @ SY349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(131,plain,
! [SV36: subst,SV5: subst] :
( ( ! [SY350: subst] :
( ( comp @ ( comp @ SV5 @ SV36 ) @ SY350 )
= ( comp @ SV5 @ ( comp @ SV36 @ SY350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(132,plain,
! [SV6: term] :
( ( var @ ( lam @ SV6 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(133,plain,
! [SV37: term,SV7: term] :
( ( ~ ( var @ ( ap @ SV7 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(134,plain,
! [SV38: subst,SV10: term] :
( ( ! [SY351: subst] :
( ( comp @ ( push @ SV10 @ SV38 ) @ SY351 )
= ( push @ ( sub @ SV10 @ SY351 ) @ ( comp @ SV38 @ SY351 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(135,plain,
! [SV39: subst,SV11: subst] :
( ( ! [SY352: subst] :
( ( comp @ ( comp @ SV11 @ SV39 ) @ SY352 )
= ( comp @ SV11 @ ( comp @ SV39 @ SY352 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(136,plain,
! [SV40: subst,SV12: term] :
( ( ( comp @ sh @ ( push @ SV12 @ SV40 ) )
= SV40 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(137,plain,
! [SV41: subst,SV14: term] :
( ( ! [SY353: subst] :
( ( sub @ ( sub @ SV14 @ SV41 ) @ SY353 )
= ( sub @ SV14 @ ( comp @ SV41 @ SY353 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(138,plain,
! [SV42: subst,SV15: term] :
( ( ( sub @ ( lam @ SV15 ) @ SV42 )
= ( lam @ ( sub @ SV15 @ ( push @ one @ ( comp @ SV42 @ sh ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(139,plain,
! [SV43: subst,SV17: term] :
( ( ( sub @ one @ ( push @ SV17 @ SV43 ) )
= SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(140,plain,
! [SV44: term,SV18: term] :
( ( ! [SY354: subst] :
( ( sub @ ( ap @ SV18 @ SV44 ) @ SY354 )
= ( ap @ ( sub @ SV18 @ SY354 ) @ ( sub @ SV44 @ SY354 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(141,plain,
( ( ! [SY355: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ sK1_SY156 @ id ) @ SY355 ) @ id ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[113]) ).
thf(142,plain,
! [SV19: subst > term > term] :
( ( ( ~ ! [SY292: subst,SY293: term,SY294: subst] :
( ( sub @ ( SV19 @ SY292 @ SY293 ) @ SY294 )
= ( SV19 @ ( comp @ SY292 @ SY294 ) @ ( sub @ SY293 @ SY294 ) ) ) )
= $true )
| ( ( ! [SY295: term,SY296: term] :
( ( lam @ ( SV19 @ sh @ one ) )
!= ( ap @ ( sub @ SY295 @ id ) @ SY296 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(143,plain,
! [SV45: term,SV20: term] :
( ( ! [SY356: term,SY357: term] :
( ( ( ap @ ( sub @ SV20 @ id ) @ SY356 )
!= ( ap @ ( sub @ SV45 @ id ) @ SY357 ) )
| ( SV20 = SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(144,plain,
! [SV21: subst > term > term] :
( ( ( ~ ! [SY300: subst,SY301: term,SY302: subst] :
( ( sub @ ( SV21 @ SY300 @ SY301 ) @ SY302 )
= ( SV21 @ ( comp @ SY300 @ SY302 ) @ ( sub @ SY301 @ SY302 ) ) ) )
= $true )
| ( ( ~ ( var @ ( sub @ ( lam @ ( SV21 @ sh @ one ) ) @ id ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(145,plain,
! [SV22: term] :
( ( ( ~ ( var @ SV22 ) )
= $true )
| ( ( var @ ( sub @ SV22 @ sh ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(146,plain,
! [SV23: subst > term > term] :
( ( ( ~ ! [SY303: subst,SY304: term,SY305: subst] :
( ( sub @ ( SV23 @ SY303 @ SY304 ) @ SY305 )
= ( SV23 @ ( comp @ SY303 @ SY305 ) @ ( sub @ SY304 @ SY305 ) ) ) )
= $true )
| ( ( ! [SY306: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SY306 @ SX2 @ SX3 ) @ SX4 )
= ( SY306 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SV23 @ sh @ one ) )
!= ( lam @ ( SY306 @ sh @ one ) ) )
| ! [SY310: subst,SY311: term] :
( ( SV23 @ SY310 @ SY311 )
= ( SY306 @ SY310 @ SY311 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(147,plain,
! [SV24: term > $o] :
( ( ( ~ ! [SY312: term,SY313: term] :
( ~ ( SV24 @ SY312 )
| ~ ( SV24 @ SY313 )
| ( SV24 @ ( ap @ SY312 @ SY313 ) ) ) )
= $true )
| ( ( ~ ! [SY314: term] :
( ~ ! [SY315: term] :
( ~ ( SV24 @ SY315 )
| ( SV24 @ ( sub @ SY314 @ ( push @ SY315 @ id ) ) ) )
| ( SV24 @ ( lam @ SY314 ) ) )
| ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(148,plain,
! [SV46: term,SV25: term] :
( ( ! [SY358: term] :
( ( lam @ SV25 )
!= ( ap @ SV46 @ SY358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(149,plain,
! [SV47: term,SV26: term] :
( ( ! [SY359: term,SY360: term] :
( ( ( ap @ SV26 @ SY359 )
!= ( ap @ SV47 @ SY360 ) )
| ( SY359 = SY360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(150,plain,
! [SV48: term,SV27: term] :
( ( ( ( sub @ SV27 @ sh )
!= ( sub @ SV48 @ sh ) )
| ( SV27 = SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(151,plain,
! [SV49: term,SV28: term] :
( ( ( ( lam @ SV28 )
!= ( lam @ SV49 ) )
| ( SV28 = SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(152,plain,
! [SV29: term > $o] :
( ( ( ~ ! [SY326: term] :
( ~ ( var @ SY326 )
| ( SV29 @ SY326 ) ) )
= $true )
| ( ( ~ ! [SY327: term,SY328: term] :
( ~ ( SV29 @ SY327 )
| ~ ( SV29 @ SY328 )
| ( SV29 @ ( ap @ SY327 @ SY328 ) ) )
| ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(153,plain,
! [SV30: term > $o] :
( ( ( ~ ( SV30 @ one ) )
= $true )
| ( ( ~ ! [SY331: term] :
( ~ ( var @ SY331 )
| ~ ( SV30 @ SY331 )
| ( SV30 @ ( sub @ SY331 @ sh ) ) )
| ! [SY332: term] :
( ~ ( var @ SY332 )
| ( SV30 @ SY332 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(154,plain,
! [SV50: term,SV31: term > $o] :
( ( ! [SY361: subst] :
( ~ ! [SY335: term] :
( ~ ( var @ SY335 )
| ( SV31 @ ( sub @ SY335 @ SY361 ) ) )
| ~ ( SV31 @ SV50 )
| ! [SY363: term] :
( ~ ( var @ SY363 )
| ( SV31 @ ( sub @ SY363 @ ( push @ SV50 @ SY361 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(155,plain,
! [SV51: term,SV32: term] :
( ( ! [SY364: term,SY365: term] :
( ( ( ap @ ( sub @ SV32 @ id ) @ SY364 )
!= ( ap @ ( sub @ SV51 @ id ) @ SY365 ) )
| ( SY364 = SY365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(156,plain,
! [SV52: term,SV33: term] :
( ( ! [SY366: term,SY367: term] :
( ( ( ap @ SV33 @ SY366 )
!= ( ap @ SV52 @ SY367 ) )
| ( SV33 = SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(157,plain,
! [SV34: term > $o] :
( ( ( ~ ! [SY343: term] :
( ~ ( var @ SY343 )
| ( SV34 @ SY343 ) ) )
= $true )
| ( ( ~ ! [SY344: term,SY345: term] :
( ~ ( SV34 @ SY344 )
| ~ ( SV34 @ SY345 )
| ( SV34 @ ( ap @ SY344 @ SY345 ) ) )
| ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(158,plain,
! [SV53: subst,SV35: subst,SV2: term] :
( ( ( sub @ ( sub @ SV2 @ SV35 ) @ SV53 )
= ( sub @ SV2 @ ( comp @ SV35 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(159,plain,
! [SV54: subst,SV36: subst,SV5: subst] :
( ( ( comp @ ( comp @ SV5 @ SV36 ) @ SV54 )
= ( comp @ SV5 @ ( comp @ SV36 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(160,plain,
! [SV37: term,SV7: term] :
( ( var @ ( ap @ SV7 @ SV37 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(161,plain,
! [SV55: subst,SV38: subst,SV10: term] :
( ( ( comp @ ( push @ SV10 @ SV38 ) @ SV55 )
= ( push @ ( sub @ SV10 @ SV55 ) @ ( comp @ SV38 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(162,plain,
! [SV56: subst,SV39: subst,SV11: subst] :
( ( ( comp @ ( comp @ SV11 @ SV39 ) @ SV56 )
= ( comp @ SV11 @ ( comp @ SV39 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(163,plain,
! [SV57: subst,SV41: subst,SV14: term] :
( ( ( sub @ ( sub @ SV14 @ SV41 ) @ SV57 )
= ( sub @ SV14 @ ( comp @ SV41 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(164,plain,
! [SV58: subst,SV44: term,SV18: term] :
( ( ( sub @ ( ap @ SV18 @ SV44 ) @ SV58 )
= ( ap @ ( sub @ SV18 @ SV58 ) @ ( sub @ SV44 @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(165,plain,
( ( ~ ( var @ ( sub @ ( ap @ ( sub @ sK1_SY156 @ id ) @ sK2_SY355 ) @ id ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[141]) ).
thf(166,plain,
! [SV19: subst > term > term] :
( ( ( ! [SY292: subst,SY293: term,SY294: subst] :
( ( sub @ ( SV19 @ SY292 @ SY293 ) @ SY294 )
= ( SV19 @ ( comp @ SY292 @ SY294 ) @ ( sub @ SY293 @ SY294 ) ) ) )
= $false )
| ( ( ! [SY295: term,SY296: term] :
( ( lam @ ( SV19 @ sh @ one ) )
!= ( ap @ ( sub @ SY295 @ id ) @ SY296 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(167,plain,
! [SV45: term,SV59: term,SV20: term] :
( ( ! [SY368: term] :
( ( ( ap @ ( sub @ SV20 @ id ) @ SV59 )
!= ( ap @ ( sub @ SV45 @ id ) @ SY368 ) )
| ( SV20 = SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(168,plain,
! [SV21: subst > term > term] :
( ( ( ! [SY300: subst,SY301: term,SY302: subst] :
( ( sub @ ( SV21 @ SY300 @ SY301 ) @ SY302 )
= ( SV21 @ ( comp @ SY300 @ SY302 ) @ ( sub @ SY301 @ SY302 ) ) ) )
= $false )
| ( ( ~ ( var @ ( sub @ ( lam @ ( SV21 @ sh @ one ) ) @ id ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(169,plain,
! [SV22: term] :
( ( ( var @ SV22 )
= $false )
| ( ( var @ ( sub @ SV22 @ sh ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(170,plain,
! [SV23: subst > term > term] :
( ( ( ! [SY303: subst,SY304: term,SY305: subst] :
( ( sub @ ( SV23 @ SY303 @ SY304 ) @ SY305 )
= ( SV23 @ ( comp @ SY303 @ SY305 ) @ ( sub @ SY304 @ SY305 ) ) ) )
= $false )
| ( ( ! [SY306: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SY306 @ SX2 @ SX3 ) @ SX4 )
= ( SY306 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SV23 @ sh @ one ) )
!= ( lam @ ( SY306 @ sh @ one ) ) )
| ! [SY310: subst,SY311: term] :
( ( SV23 @ SY310 @ SY311 )
= ( SY306 @ SY310 @ SY311 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(171,plain,
! [SV24: term > $o] :
( ( ( ! [SY312: term,SY313: term] :
( ~ ( SV24 @ SY312 )
| ~ ( SV24 @ SY313 )
| ( SV24 @ ( ap @ SY312 @ SY313 ) ) ) )
= $false )
| ( ( ~ ! [SY314: term] :
( ~ ! [SY315: term] :
( ~ ( SV24 @ SY315 )
| ( SV24 @ ( sub @ SY314 @ ( push @ SY315 @ id ) ) ) )
| ( SV24 @ ( lam @ SY314 ) ) )
| ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(172,plain,
! [SV60: term,SV46: term,SV25: term] :
( ( ( lam @ SV25 )
!= ( ap @ SV46 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(173,plain,
! [SV47: term,SV61: term,SV26: term] :
( ( ! [SY369: term] :
( ( ( ap @ SV26 @ SV61 )
!= ( ap @ SV47 @ SY369 ) )
| ( SV61 = SY369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(174,plain,
! [SV48: term,SV27: term] :
( ( ( ( sub @ SV27 @ sh )
!= ( sub @ SV48 @ sh ) )
= $true )
| ( ( SV27 = SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(175,plain,
! [SV49: term,SV28: term] :
( ( ( ( lam @ SV28 )
!= ( lam @ SV49 ) )
= $true )
| ( ( SV28 = SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(176,plain,
! [SV29: term > $o] :
( ( ( ! [SY326: term] :
( ~ ( var @ SY326 )
| ( SV29 @ SY326 ) ) )
= $false )
| ( ( ~ ! [SY327: term,SY328: term] :
( ~ ( SV29 @ SY327 )
| ~ ( SV29 @ SY328 )
| ( SV29 @ ( ap @ SY327 @ SY328 ) ) )
| ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(177,plain,
! [SV30: term > $o] :
( ( ( SV30 @ one )
= $false )
| ( ( ~ ! [SY331: term] :
( ~ ( var @ SY331 )
| ~ ( SV30 @ SY331 )
| ( SV30 @ ( sub @ SY331 @ sh ) ) )
| ! [SY332: term] :
( ~ ( var @ SY332 )
| ( SV30 @ SY332 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(178,plain,
! [SV50: term,SV62: subst,SV31: term > $o] :
( ( ~ ! [SY370: term] :
( ~ ( var @ SY370 )
| ( SV31 @ ( sub @ SY370 @ SV62 ) ) )
| ~ ( SV31 @ SV50 )
| ! [SY371: term] :
( ~ ( var @ SY371 )
| ( SV31 @ ( sub @ SY371 @ ( push @ SV50 @ SV62 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(179,plain,
! [SV51: term,SV63: term,SV32: term] :
( ( ! [SY372: term] :
( ( ( ap @ ( sub @ SV32 @ id ) @ SV63 )
!= ( ap @ ( sub @ SV51 @ id ) @ SY372 ) )
| ( SV63 = SY372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(180,plain,
! [SV52: term,SV64: term,SV33: term] :
( ( ! [SY373: term] :
( ( ( ap @ SV33 @ SV64 )
!= ( ap @ SV52 @ SY373 ) )
| ( SV33 = SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(181,plain,
! [SV34: term > $o] :
( ( ( ! [SY343: term] :
( ~ ( var @ SY343 )
| ( SV34 @ SY343 ) ) )
= $false )
| ( ( ~ ! [SY344: term,SY345: term] :
( ~ ( SV34 @ SY344 )
| ~ ( SV34 @ SY345 )
| ( SV34 @ ( ap @ SY344 @ SY345 ) ) )
| ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(182,plain,
( ( var @ ( sub @ ( ap @ ( sub @ sK1_SY156 @ id ) @ sK2_SY355 ) @ id ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(183,plain,
! [SV19: subst > term > term] :
( ( ( ! [SY374: term,SY375: subst] :
( ( sub @ ( SV19 @ ( sK3_SY292 @ SV19 ) @ SY374 ) @ SY375 )
= ( SV19 @ ( comp @ ( sK3_SY292 @ SV19 ) @ SY375 ) @ ( sub @ SY374 @ SY375 ) ) ) )
= $false )
| ( ( ! [SY295: term,SY296: term] :
( ( lam @ ( SV19 @ sh @ one ) )
!= ( ap @ ( sub @ SY295 @ id ) @ SY296 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[166]) ).
thf(184,plain,
! [SV65: term,SV45: term,SV59: term,SV20: term] :
( ( ( ( ap @ ( sub @ SV20 @ id ) @ SV59 )
!= ( ap @ ( sub @ SV45 @ id ) @ SV65 ) )
| ( SV20 = SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(185,plain,
! [SV21: subst > term > term] :
( ( ( ! [SY376: term,SY377: subst] :
( ( sub @ ( SV21 @ ( sK4_SY300 @ SV21 ) @ SY376 ) @ SY377 )
= ( SV21 @ ( comp @ ( sK4_SY300 @ SV21 ) @ SY377 ) @ ( sub @ SY376 @ SY377 ) ) ) )
= $false )
| ( ( ~ ( var @ ( sub @ ( lam @ ( SV21 @ sh @ one ) ) @ id ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[168]) ).
thf(186,plain,
! [SV23: subst > term > term] :
( ( ( ! [SY378: term,SY379: subst] :
( ( sub @ ( SV23 @ ( sK5_SY303 @ SV23 ) @ SY378 ) @ SY379 )
= ( SV23 @ ( comp @ ( sK5_SY303 @ SV23 ) @ SY379 ) @ ( sub @ SY378 @ SY379 ) ) ) )
= $false )
| ( ( ! [SY306: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SY306 @ SX2 @ SX3 ) @ SX4 )
= ( SY306 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SV23 @ sh @ one ) )
!= ( lam @ ( SY306 @ sh @ one ) ) )
| ! [SY310: subst,SY311: term] :
( ( SV23 @ SY310 @ SY311 )
= ( SY306 @ SY310 @ SY311 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[170]) ).
thf(187,plain,
! [SV24: term > $o] :
( ( ( ! [SY380: term] :
( ~ ( SV24 @ ( sK6_SY312 @ SV24 ) )
| ~ ( SV24 @ SY380 )
| ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ SY380 ) ) ) )
= $false )
| ( ( ~ ! [SY314: term] :
( ~ ! [SY315: term] :
( ~ ( SV24 @ SY315 )
| ( SV24 @ ( sub @ SY314 @ ( push @ SY315 @ id ) ) ) )
| ( SV24 @ ( lam @ SY314 ) ) )
| ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[171]) ).
thf(188,plain,
! [SV60: term,SV46: term,SV25: term] :
( ( ( lam @ SV25 )
= ( ap @ SV46 @ SV60 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(189,plain,
! [SV66: term,SV47: term,SV61: term,SV26: term] :
( ( ( ( ap @ SV26 @ SV61 )
!= ( ap @ SV47 @ SV66 ) )
| ( SV61 = SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(190,plain,
! [SV48: term,SV27: term] :
( ( ( ( sub @ SV27 @ sh )
= ( sub @ SV48 @ sh ) )
= $false )
| ( ( SV27 = SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(191,plain,
! [SV49: term,SV28: term] :
( ( ( ( lam @ SV28 )
= ( lam @ SV49 ) )
= $false )
| ( ( SV28 = SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(192,plain,
! [SV29: term > $o] :
( ( ( ~ ( var @ ( sK7_SY326 @ SV29 ) )
| ( SV29 @ ( sK7_SY326 @ SV29 ) ) )
= $false )
| ( ( ~ ! [SY327: term,SY328: term] :
( ~ ( SV29 @ SY327 )
| ~ ( SV29 @ SY328 )
| ( SV29 @ ( ap @ SY327 @ SY328 ) ) )
| ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[176]) ).
thf(193,plain,
! [SV30: term > $o] :
( ( ( ~ ! [SY331: term] :
( ~ ( var @ SY331 )
| ~ ( SV30 @ SY331 )
| ( SV30 @ ( sub @ SY331 @ sh ) ) ) )
= $true )
| ( ( ! [SY332: term] :
( ~ ( var @ SY332 )
| ( SV30 @ SY332 ) ) )
= $true )
| ( ( SV30 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(194,plain,
! [SV50: term,SV62: subst,SV31: term > $o] :
( ( ( ~ ! [SY370: term] :
( ~ ( var @ SY370 )
| ( SV31 @ ( sub @ SY370 @ SV62 ) ) ) )
= $true )
| ( ( ~ ( SV31 @ SV50 )
| ! [SY371: term] :
( ~ ( var @ SY371 )
| ( SV31 @ ( sub @ SY371 @ ( push @ SV50 @ SV62 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(195,plain,
! [SV67: term,SV51: term,SV63: term,SV32: term] :
( ( ( ( ap @ ( sub @ SV32 @ id ) @ SV63 )
!= ( ap @ ( sub @ SV51 @ id ) @ SV67 ) )
| ( SV63 = SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(196,plain,
! [SV68: term,SV52: term,SV64: term,SV33: term] :
( ( ( ( ap @ SV33 @ SV64 )
!= ( ap @ SV52 @ SV68 ) )
| ( SV33 = SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(197,plain,
! [SV34: term > $o] :
( ( ( ~ ( var @ ( sK8_SY343 @ SV34 ) )
| ( SV34 @ ( sK8_SY343 @ SV34 ) ) )
= $false )
| ( ( ~ ! [SY344: term,SY345: term] :
( ~ ( SV34 @ SY344 )
| ~ ( SV34 @ SY345 )
| ( SV34 @ ( ap @ SY344 @ SY345 ) ) )
| ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[181]) ).
thf(198,plain,
! [SV19: subst > term > term] :
( ( ( ! [SY381: subst] :
( ( sub @ ( SV19 @ ( sK3_SY292 @ SV19 ) @ ( sK9_SY374 @ SV19 ) ) @ SY381 )
= ( SV19 @ ( comp @ ( sK3_SY292 @ SV19 ) @ SY381 ) @ ( sub @ ( sK9_SY374 @ SV19 ) @ SY381 ) ) ) )
= $false )
| ( ( ! [SY295: term,SY296: term] :
( ( lam @ ( SV19 @ sh @ one ) )
!= ( ap @ ( sub @ SY295 @ id ) @ SY296 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[183]) ).
thf(199,plain,
! [SV65: term,SV45: term,SV59: term,SV20: term] :
( ( ( ( ap @ ( sub @ SV20 @ id ) @ SV59 )
!= ( ap @ ( sub @ SV45 @ id ) @ SV65 ) )
= $true )
| ( ( SV20 = SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(200,plain,
! [SV21: subst > term > term] :
( ( ( ! [SY382: subst] :
( ( sub @ ( SV21 @ ( sK4_SY300 @ SV21 ) @ ( sK10_SY376 @ SV21 ) ) @ SY382 )
= ( SV21 @ ( comp @ ( sK4_SY300 @ SV21 ) @ SY382 ) @ ( sub @ ( sK10_SY376 @ SV21 ) @ SY382 ) ) ) )
= $false )
| ( ( ~ ( var @ ( sub @ ( lam @ ( SV21 @ sh @ one ) ) @ id ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[185]) ).
thf(201,plain,
! [SV23: subst > term > term] :
( ( ( ! [SY383: subst] :
( ( sub @ ( SV23 @ ( sK5_SY303 @ SV23 ) @ ( sK11_SY378 @ SV23 ) ) @ SY383 )
= ( SV23 @ ( comp @ ( sK5_SY303 @ SV23 ) @ SY383 ) @ ( sub @ ( sK11_SY378 @ SV23 ) @ SY383 ) ) ) )
= $false )
| ( ( ! [SY306: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SY306 @ SX2 @ SX3 ) @ SX4 )
= ( SY306 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SV23 @ sh @ one ) )
!= ( lam @ ( SY306 @ sh @ one ) ) )
| ! [SY310: subst,SY311: term] :
( ( SV23 @ SY310 @ SY311 )
= ( SY306 @ SY310 @ SY311 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[186]) ).
thf(202,plain,
! [SV24: term > $o] :
( ( ( ~ ( SV24 @ ( sK6_SY312 @ SV24 ) )
| ~ ( SV24 @ ( sK12_SY380 @ SV24 ) )
| ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) ) )
= $false )
| ( ( ~ ! [SY314: term] :
( ~ ! [SY315: term] :
( ~ ( SV24 @ SY315 )
| ( SV24 @ ( sub @ SY314 @ ( push @ SY315 @ id ) ) ) )
| ( SV24 @ ( lam @ SY314 ) ) )
| ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[187]) ).
thf(203,plain,
! [SV66: term,SV47: term,SV61: term,SV26: term] :
( ( ( ( ap @ SV26 @ SV61 )
!= ( ap @ SV47 @ SV66 ) )
= $true )
| ( ( SV61 = SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(204,plain,
! [SV29: term > $o] :
( ( ( ~ ( var @ ( sK7_SY326 @ SV29 ) ) )
= $false )
| ( ( ~ ! [SY327: term,SY328: term] :
( ~ ( SV29 @ SY327 )
| ~ ( SV29 @ SY328 )
| ( SV29 @ ( ap @ SY327 @ SY328 ) ) )
| ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(205,plain,
! [SV29: term > $o] :
( ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false )
| ( ( ~ ! [SY327: term,SY328: term] :
( ~ ( SV29 @ SY327 )
| ~ ( SV29 @ SY328 )
| ( SV29 @ ( ap @ SY327 @ SY328 ) ) )
| ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(206,plain,
! [SV30: term > $o] :
( ( ( ! [SY331: term] :
( ~ ( var @ SY331 )
| ~ ( SV30 @ SY331 )
| ( SV30 @ ( sub @ SY331 @ sh ) ) ) )
= $false )
| ( ( ! [SY332: term] :
( ~ ( var @ SY332 )
| ( SV30 @ SY332 ) ) )
= $true )
| ( ( SV30 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(207,plain,
! [SV50: term,SV62: subst,SV31: term > $o] :
( ( ( ! [SY370: term] :
( ~ ( var @ SY370 )
| ( SV31 @ ( sub @ SY370 @ SV62 ) ) ) )
= $false )
| ( ( ~ ( SV31 @ SV50 )
| ! [SY371: term] :
( ~ ( var @ SY371 )
| ( SV31 @ ( sub @ SY371 @ ( push @ SV50 @ SV62 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(208,plain,
! [SV67: term,SV51: term,SV63: term,SV32: term] :
( ( ( ( ap @ ( sub @ SV32 @ id ) @ SV63 )
!= ( ap @ ( sub @ SV51 @ id ) @ SV67 ) )
= $true )
| ( ( SV63 = SV67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(209,plain,
! [SV68: term,SV52: term,SV64: term,SV33: term] :
( ( ( ( ap @ SV33 @ SV64 )
!= ( ap @ SV52 @ SV68 ) )
= $true )
| ( ( SV33 = SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(210,plain,
! [SV34: term > $o] :
( ( ( ~ ( var @ ( sK8_SY343 @ SV34 ) ) )
= $false )
| ( ( ~ ! [SY344: term,SY345: term] :
( ~ ( SV34 @ SY344 )
| ~ ( SV34 @ SY345 )
| ( SV34 @ ( ap @ SY344 @ SY345 ) ) )
| ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(211,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false )
| ( ( ~ ! [SY344: term,SY345: term] :
( ~ ( SV34 @ SY344 )
| ~ ( SV34 @ SY345 )
| ( SV34 @ ( ap @ SY344 @ SY345 ) ) )
| ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(212,plain,
! [SV19: subst > term > term] :
( ( ( ( sub @ ( SV19 @ ( sK3_SY292 @ SV19 ) @ ( sK9_SY374 @ SV19 ) ) @ ( sK13_SY381 @ SV19 ) )
= ( SV19 @ ( comp @ ( sK3_SY292 @ SV19 ) @ ( sK13_SY381 @ SV19 ) ) @ ( sub @ ( sK9_SY374 @ SV19 ) @ ( sK13_SY381 @ SV19 ) ) ) )
= $false )
| ( ( ! [SY295: term,SY296: term] :
( ( lam @ ( SV19 @ sh @ one ) )
!= ( ap @ ( sub @ SY295 @ id ) @ SY296 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[198]) ).
thf(213,plain,
! [SV65: term,SV45: term,SV59: term,SV20: term] :
( ( ( ( ap @ ( sub @ SV20 @ id ) @ SV59 )
= ( ap @ ( sub @ SV45 @ id ) @ SV65 ) )
= $false )
| ( ( SV20 = SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(214,plain,
! [SV21: subst > term > term] :
( ( ( ( sub @ ( SV21 @ ( sK4_SY300 @ SV21 ) @ ( sK10_SY376 @ SV21 ) ) @ ( sK14_SY382 @ SV21 ) )
= ( SV21 @ ( comp @ ( sK4_SY300 @ SV21 ) @ ( sK14_SY382 @ SV21 ) ) @ ( sub @ ( sK10_SY376 @ SV21 ) @ ( sK14_SY382 @ SV21 ) ) ) )
= $false )
| ( ( ~ ( var @ ( sub @ ( lam @ ( SV21 @ sh @ one ) ) @ id ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[200]) ).
thf(215,plain,
! [SV23: subst > term > term] :
( ( ( ( sub @ ( SV23 @ ( sK5_SY303 @ SV23 ) @ ( sK11_SY378 @ SV23 ) ) @ ( sK15_SY383 @ SV23 ) )
= ( SV23 @ ( comp @ ( sK5_SY303 @ SV23 ) @ ( sK15_SY383 @ SV23 ) ) @ ( sub @ ( sK11_SY378 @ SV23 ) @ ( sK15_SY383 @ SV23 ) ) ) )
= $false )
| ( ( ! [SY306: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SY306 @ SX2 @ SX3 ) @ SX4 )
= ( SY306 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SV23 @ sh @ one ) )
!= ( lam @ ( SY306 @ sh @ one ) ) )
| ! [SY310: subst,SY311: term] :
( ( SV23 @ SY310 @ SY311 )
= ( SY306 @ SY310 @ SY311 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[201]) ).
thf(216,plain,
! [SV24: term > $o] :
( ( ( ~ ( SV24 @ ( sK6_SY312 @ SV24 ) ) )
= $false )
| ( ( ~ ! [SY314: term] :
( ~ ! [SY315: term] :
( ~ ( SV24 @ SY315 )
| ( SV24 @ ( sub @ SY314 @ ( push @ SY315 @ id ) ) ) )
| ( SV24 @ ( lam @ SY314 ) ) )
| ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(217,plain,
! [SV24: term > $o] :
( ( ( ~ ( SV24 @ ( sK12_SY380 @ SV24 ) )
| ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) ) )
= $false )
| ( ( ~ ! [SY314: term] :
( ~ ! [SY315: term] :
( ~ ( SV24 @ SY315 )
| ( SV24 @ ( sub @ SY314 @ ( push @ SY315 @ id ) ) ) )
| ( SV24 @ ( lam @ SY314 ) ) )
| ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(218,plain,
! [SV66: term,SV47: term,SV61: term,SV26: term] :
( ( ( ( ap @ SV26 @ SV61 )
= ( ap @ SV47 @ SV66 ) )
= $false )
| ( ( SV61 = SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(219,plain,
! [SV29: term > $o] :
( ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true )
| ( ( ~ ! [SY327: term,SY328: term] :
( ~ ( SV29 @ SY327 )
| ~ ( SV29 @ SY328 )
| ( SV29 @ ( ap @ SY327 @ SY328 ) ) )
| ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(220,plain,
! [SV29: term > $o] :
( ( ( ~ ! [SY327: term,SY328: term] :
( ~ ( SV29 @ SY327 )
| ~ ( SV29 @ SY328 )
| ( SV29 @ ( ap @ SY327 @ SY328 ) ) ) )
= $true )
| ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(221,plain,
! [SV30: term > $o] :
( ( ( ~ ( var @ ( sK16_SY331 @ SV30 ) )
| ~ ( SV30 @ ( sK16_SY331 @ SV30 ) )
| ( SV30 @ ( sub @ ( sK16_SY331 @ SV30 ) @ sh ) ) )
= $false )
| ( ( ! [SY332: term] :
( ~ ( var @ SY332 )
| ( SV30 @ SY332 ) ) )
= $true )
| ( ( SV30 @ one )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[206]) ).
thf(222,plain,
! [SV31: term > $o,SV62: subst,SV50: term] :
( ( ( ~ ( var @ ( sK17_SY370 @ SV50 @ SV62 @ SV31 ) )
| ( SV31 @ ( sub @ ( sK17_SY370 @ SV50 @ SV62 @ SV31 ) @ SV62 ) ) )
= $false )
| ( ( ~ ( SV31 @ SV50 )
| ! [SY371: term] :
( ~ ( var @ SY371 )
| ( SV31 @ ( sub @ SY371 @ ( push @ SV50 @ SV62 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[207]) ).
thf(223,plain,
! [SV67: term,SV51: term,SV63: term,SV32: term] :
( ( ( ( ap @ ( sub @ SV32 @ id ) @ SV63 )
= ( ap @ ( sub @ SV51 @ id ) @ SV67 ) )
= $false )
| ( ( SV63 = SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(224,plain,
! [SV68: term,SV52: term,SV64: term,SV33: term] :
( ( ( ( ap @ SV33 @ SV64 )
= ( ap @ SV52 @ SV68 ) )
= $false )
| ( ( SV33 = SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(225,plain,
! [SV34: term > $o] :
( ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true )
| ( ( ~ ! [SY344: term,SY345: term] :
( ~ ( SV34 @ SY344 )
| ~ ( SV34 @ SY345 )
| ( SV34 @ ( ap @ SY344 @ SY345 ) ) )
| ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(226,plain,
! [SV34: term > $o] :
( ( ( ~ ! [SY344: term,SY345: term] :
( ~ ( SV34 @ SY344 )
| ~ ( SV34 @ SY345 )
| ( SV34 @ ( ap @ SY344 @ SY345 ) ) ) )
= $true )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(227,plain,
! [SV69: term,SV19: subst > term > term] :
( ( ( ! [SY384: term] :
( ( lam @ ( SV19 @ sh @ one ) )
!= ( ap @ ( sub @ SV69 @ id ) @ SY384 ) ) )
= $true )
| ( ( ( sub @ ( SV19 @ ( sK3_SY292 @ SV19 ) @ ( sK9_SY374 @ SV19 ) ) @ ( sK13_SY381 @ SV19 ) )
= ( SV19 @ ( comp @ ( sK3_SY292 @ SV19 ) @ ( sK13_SY381 @ SV19 ) ) @ ( sub @ ( sK9_SY374 @ SV19 ) @ ( sK13_SY381 @ SV19 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(228,plain,
! [SV21: subst > term > term] :
( ( ( var @ ( sub @ ( lam @ ( SV21 @ sh @ one ) ) @ id ) )
= $false )
| ( ( ( sub @ ( SV21 @ ( sK4_SY300 @ SV21 ) @ ( sK10_SY376 @ SV21 ) ) @ ( sK14_SY382 @ SV21 ) )
= ( SV21 @ ( comp @ ( sK4_SY300 @ SV21 ) @ ( sK14_SY382 @ SV21 ) ) @ ( sub @ ( sK10_SY376 @ SV21 ) @ ( sK14_SY382 @ SV21 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(229,plain,
! [SV23: subst > term > term,SV70: subst > term > term] :
( ( ( ~ ! [SY385: subst,SY386: term,SY387: subst] :
( ( sub @ ( SV70 @ SY385 @ SY386 ) @ SY387 )
= ( SV70 @ ( comp @ SY385 @ SY387 ) @ ( sub @ SY386 @ SY387 ) ) )
| ( ( lam @ ( SV23 @ sh @ one ) )
!= ( lam @ ( SV70 @ sh @ one ) ) )
| ! [SY388: subst,SY389: term] :
( ( SV23 @ SY388 @ SY389 )
= ( SV70 @ SY388 @ SY389 ) ) )
= $true )
| ( ( ( sub @ ( SV23 @ ( sK5_SY303 @ SV23 ) @ ( sK11_SY378 @ SV23 ) ) @ ( sK15_SY383 @ SV23 ) )
= ( SV23 @ ( comp @ ( sK5_SY303 @ SV23 ) @ ( sK15_SY383 @ SV23 ) ) @ ( sub @ ( sK11_SY378 @ SV23 ) @ ( sK15_SY383 @ SV23 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(230,plain,
! [SV24: term > $o] :
( ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true )
| ( ( ~ ! [SY314: term] :
( ~ ! [SY315: term] :
( ~ ( SV24 @ SY315 )
| ( SV24 @ ( sub @ SY314 @ ( push @ SY315 @ id ) ) ) )
| ( SV24 @ ( lam @ SY314 ) ) )
| ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(231,plain,
! [SV24: term > $o] :
( ( ( ~ ( SV24 @ ( sK12_SY380 @ SV24 ) ) )
= $false )
| ( ( ~ ! [SY314: term] :
( ~ ! [SY315: term] :
( ~ ( SV24 @ SY315 )
| ( SV24 @ ( sub @ SY314 @ ( push @ SY315 @ id ) ) ) )
| ( SV24 @ ( lam @ SY314 ) ) )
| ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(232,plain,
! [SV24: term > $o] :
( ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false )
| ( ( ~ ! [SY314: term] :
( ~ ! [SY315: term] :
( ~ ( SV24 @ SY315 )
| ( SV24 @ ( sub @ SY314 @ ( push @ SY315 @ id ) ) ) )
| ( SV24 @ ( lam @ SY314 ) ) )
| ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(233,plain,
! [SV29: term > $o] :
( ( ( ~ ! [SY327: term,SY328: term] :
( ~ ( SV29 @ SY327 )
| ~ ( SV29 @ SY328 )
| ( SV29 @ ( ap @ SY327 @ SY328 ) ) ) )
= $true )
| ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(234,plain,
! [SV29: term > $o] :
( ( ( ! [SY327: term,SY328: term] :
( ~ ( SV29 @ SY327 )
| ~ ( SV29 @ SY328 )
| ( SV29 @ ( ap @ SY327 @ SY328 ) ) ) )
= $false )
| ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(235,plain,
! [SV30: term > $o] :
( ( ( ~ ( var @ ( sK16_SY331 @ SV30 ) ) )
= $false )
| ( ( ! [SY332: term] :
( ~ ( var @ SY332 )
| ( SV30 @ SY332 ) ) )
= $true )
| ( ( SV30 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(236,plain,
! [SV30: term > $o] :
( ( ( ~ ( SV30 @ ( sK16_SY331 @ SV30 ) )
| ( SV30 @ ( sub @ ( sK16_SY331 @ SV30 ) @ sh ) ) )
= $false )
| ( ( ! [SY332: term] :
( ~ ( var @ SY332 )
| ( SV30 @ SY332 ) ) )
= $true )
| ( ( SV30 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(237,plain,
! [SV31: term > $o,SV62: subst,SV50: term] :
( ( ( ~ ( var @ ( sK17_SY370 @ SV50 @ SV62 @ SV31 ) ) )
= $false )
| ( ( ~ ( SV31 @ SV50 )
| ! [SY371: term] :
( ~ ( var @ SY371 )
| ( SV31 @ ( sub @ SY371 @ ( push @ SV50 @ SV62 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(238,plain,
! [SV62: subst,SV50: term,SV31: term > $o] :
( ( ( SV31 @ ( sub @ ( sK17_SY370 @ SV50 @ SV62 @ SV31 ) @ SV62 ) )
= $false )
| ( ( ~ ( SV31 @ SV50 )
| ! [SY371: term] :
( ~ ( var @ SY371 )
| ( SV31 @ ( sub @ SY371 @ ( push @ SV50 @ SV62 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(239,plain,
! [SV34: term > $o] :
( ( ( ~ ! [SY344: term,SY345: term] :
( ~ ( SV34 @ SY344 )
| ~ ( SV34 @ SY345 )
| ( SV34 @ ( ap @ SY344 @ SY345 ) ) ) )
= $true )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(240,plain,
! [SV34: term > $o] :
( ( ( ! [SY344: term,SY345: term] :
( ~ ( SV34 @ SY344 )
| ~ ( SV34 @ SY345 )
| ( SV34 @ ( ap @ SY344 @ SY345 ) ) ) )
= $false )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(241,plain,
! [SV71: term,SV69: term,SV19: subst > term > term] :
( ( ( ( lam @ ( SV19 @ sh @ one ) )
!= ( ap @ ( sub @ SV69 @ id ) @ SV71 ) )
= $true )
| ( ( ( sub @ ( SV19 @ ( sK3_SY292 @ SV19 ) @ ( sK9_SY374 @ SV19 ) ) @ ( sK13_SY381 @ SV19 ) )
= ( SV19 @ ( comp @ ( sK3_SY292 @ SV19 ) @ ( sK13_SY381 @ SV19 ) ) @ ( sub @ ( sK9_SY374 @ SV19 ) @ ( sK13_SY381 @ SV19 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(242,plain,
! [SV23: subst > term > term,SV70: subst > term > term] :
( ( ( ~ ! [SY385: subst,SY386: term,SY387: subst] :
( ( sub @ ( SV70 @ SY385 @ SY386 ) @ SY387 )
= ( SV70 @ ( comp @ SY385 @ SY387 ) @ ( sub @ SY386 @ SY387 ) ) ) )
= $true )
| ( ( ( ( lam @ ( SV23 @ sh @ one ) )
!= ( lam @ ( SV70 @ sh @ one ) ) )
| ! [SY388: subst,SY389: term] :
( ( SV23 @ SY388 @ SY389 )
= ( SV70 @ SY388 @ SY389 ) ) )
= $true )
| ( ( ( sub @ ( SV23 @ ( sK5_SY303 @ SV23 ) @ ( sK11_SY378 @ SV23 ) ) @ ( sK15_SY383 @ SV23 ) )
= ( SV23 @ ( comp @ ( sK5_SY303 @ SV23 ) @ ( sK15_SY383 @ SV23 ) ) @ ( sub @ ( sK11_SY378 @ SV23 ) @ ( sK15_SY383 @ SV23 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(243,plain,
! [SV24: term > $o] :
( ( ( ~ ! [SY314: term] :
( ~ ! [SY315: term] :
( ~ ( SV24 @ SY315 )
| ( SV24 @ ( sub @ SY314 @ ( push @ SY315 @ id ) ) ) )
| ( SV24 @ ( lam @ SY314 ) ) ) )
= $true )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(244,plain,
! [SV24: term > $o] :
( ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true )
| ( ( ~ ! [SY314: term] :
( ~ ! [SY315: term] :
( ~ ( SV24 @ SY315 )
| ( SV24 @ ( sub @ SY314 @ ( push @ SY315 @ id ) ) ) )
| ( SV24 @ ( lam @ SY314 ) ) )
| ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(245,plain,
! [SV24: term > $o] :
( ( ( ~ ! [SY314: term] :
( ~ ! [SY315: term] :
( ~ ( SV24 @ SY315 )
| ( SV24 @ ( sub @ SY314 @ ( push @ SY315 @ id ) ) ) )
| ( SV24 @ ( lam @ SY314 ) ) ) )
= $true )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(246,plain,
! [SV29: term > $o] :
( ( ( ! [SY327: term,SY328: term] :
( ~ ( SV29 @ SY327 )
| ~ ( SV29 @ SY328 )
| ( SV29 @ ( ap @ SY327 @ SY328 ) ) ) )
= $false )
| ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(247,plain,
! [SV29: term > $o] :
( ( ( ! [SY390: term] :
( ~ ( SV29 @ ( sK18_SY327 @ SV29 ) )
| ~ ( SV29 @ SY390 )
| ( SV29 @ ( ap @ ( sK18_SY327 @ SV29 ) @ SY390 ) ) ) )
= $false )
| ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[234]) ).
thf(248,plain,
! [SV30: term > $o] :
( ( ( var @ ( sK16_SY331 @ SV30 ) )
= $true )
| ( ( ! [SY332: term] :
( ~ ( var @ SY332 )
| ( SV30 @ SY332 ) ) )
= $true )
| ( ( SV30 @ one )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(249,plain,
! [SV30: term > $o] :
( ( ( ~ ( SV30 @ ( sK16_SY331 @ SV30 ) ) )
= $false )
| ( ( ! [SY332: term] :
( ~ ( var @ SY332 )
| ( SV30 @ SY332 ) ) )
= $true )
| ( ( SV30 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(250,plain,
! [SV30: term > $o] :
( ( ( SV30 @ ( sub @ ( sK16_SY331 @ SV30 ) @ sh ) )
= $false )
| ( ( ! [SY332: term] :
( ~ ( var @ SY332 )
| ( SV30 @ SY332 ) ) )
= $true )
| ( ( SV30 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(251,plain,
! [SV31: term > $o,SV62: subst,SV50: term] :
( ( ( var @ ( sK17_SY370 @ SV50 @ SV62 @ SV31 ) )
= $true )
| ( ( ~ ( SV31 @ SV50 )
| ! [SY371: term] :
( ~ ( var @ SY371 )
| ( SV31 @ ( sub @ SY371 @ ( push @ SV50 @ SV62 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(252,plain,
! [SV62: subst,SV50: term,SV31: term > $o] :
( ( ( ~ ( SV31 @ SV50 ) )
= $true )
| ( ( ! [SY371: term] :
( ~ ( var @ SY371 )
| ( SV31 @ ( sub @ SY371 @ ( push @ SV50 @ SV62 ) ) ) ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK17_SY370 @ SV50 @ SV62 @ SV31 ) @ SV62 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(253,plain,
! [SV34: term > $o] :
( ( ( ! [SY344: term,SY345: term] :
( ~ ( SV34 @ SY344 )
| ~ ( SV34 @ SY345 )
| ( SV34 @ ( ap @ SY344 @ SY345 ) ) ) )
= $false )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(254,plain,
! [SV34: term > $o] :
( ( ( ! [SY391: term] :
( ~ ( SV34 @ ( sK19_SY344 @ SV34 ) )
| ~ ( SV34 @ SY391 )
| ( SV34 @ ( ap @ ( sK19_SY344 @ SV34 ) @ SY391 ) ) ) )
= $false )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[240]) ).
thf(255,plain,
! [SV71: term,SV69: term,SV19: subst > term > term] :
( ( ( ( lam @ ( SV19 @ sh @ one ) )
= ( ap @ ( sub @ SV69 @ id ) @ SV71 ) )
= $false )
| ( ( ( sub @ ( SV19 @ ( sK3_SY292 @ SV19 ) @ ( sK9_SY374 @ SV19 ) ) @ ( sK13_SY381 @ SV19 ) )
= ( SV19 @ ( comp @ ( sK3_SY292 @ SV19 ) @ ( sK13_SY381 @ SV19 ) ) @ ( sub @ ( sK9_SY374 @ SV19 ) @ ( sK13_SY381 @ SV19 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(256,plain,
! [SV23: subst > term > term,SV70: subst > term > term] :
( ( ( ! [SY385: subst,SY386: term,SY387: subst] :
( ( sub @ ( SV70 @ SY385 @ SY386 ) @ SY387 )
= ( SV70 @ ( comp @ SY385 @ SY387 ) @ ( sub @ SY386 @ SY387 ) ) ) )
= $false )
| ( ( ( ( lam @ ( SV23 @ sh @ one ) )
!= ( lam @ ( SV70 @ sh @ one ) ) )
| ! [SY388: subst,SY389: term] :
( ( SV23 @ SY388 @ SY389 )
= ( SV70 @ SY388 @ SY389 ) ) )
= $true )
| ( ( ( sub @ ( SV23 @ ( sK5_SY303 @ SV23 ) @ ( sK11_SY378 @ SV23 ) ) @ ( sK15_SY383 @ SV23 ) )
= ( SV23 @ ( comp @ ( sK5_SY303 @ SV23 ) @ ( sK15_SY383 @ SV23 ) ) @ ( sub @ ( sK11_SY378 @ SV23 ) @ ( sK15_SY383 @ SV23 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(257,plain,
! [SV24: term > $o] :
( ( ( ! [SY314: term] :
( ~ ! [SY315: term] :
( ~ ( SV24 @ SY315 )
| ( SV24 @ ( sub @ SY314 @ ( push @ SY315 @ id ) ) ) )
| ( SV24 @ ( lam @ SY314 ) ) ) )
= $false )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(258,plain,
! [SV24: term > $o] :
( ( ( ~ ! [SY314: term] :
( ~ ! [SY315: term] :
( ~ ( SV24 @ SY315 )
| ( SV24 @ ( sub @ SY314 @ ( push @ SY315 @ id ) ) ) )
| ( SV24 @ ( lam @ SY314 ) ) ) )
= $true )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(259,plain,
! [SV24: term > $o] :
( ( ( ! [SY314: term] :
( ~ ! [SY315: term] :
( ~ ( SV24 @ SY315 )
| ( SV24 @ ( sub @ SY314 @ ( push @ SY315 @ id ) ) ) )
| ( SV24 @ ( lam @ SY314 ) ) ) )
= $false )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(260,plain,
! [SV29: term > $o] :
( ( ( ! [SY392: term] :
( ~ ( SV29 @ ( sK20_SY327 @ SV29 ) )
| ~ ( SV29 @ SY392 )
| ( SV29 @ ( ap @ ( sK20_SY327 @ SV29 ) @ SY392 ) ) ) )
= $false )
| ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[246]) ).
thf(261,plain,
! [SV29: term > $o] :
( ( ( ~ ( SV29 @ ( sK18_SY327 @ SV29 ) )
| ~ ( SV29 @ ( sK21_SY390 @ SV29 ) )
| ( SV29 @ ( ap @ ( sK18_SY327 @ SV29 ) @ ( sK21_SY390 @ SV29 ) ) ) )
= $false )
| ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[247]) ).
thf(262,plain,
! [SV30: term > $o,SV72: term] :
( ( ( ~ ( var @ SV72 )
| ( SV30 @ SV72 ) )
= $true )
| ( ( var @ ( sK16_SY331 @ SV30 ) )
= $true )
| ( ( SV30 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(263,plain,
! [SV30: term > $o] :
( ( ( SV30 @ ( sK16_SY331 @ SV30 ) )
= $true )
| ( ( ! [SY332: term] :
( ~ ( var @ SY332 )
| ( SV30 @ SY332 ) ) )
= $true )
| ( ( SV30 @ one )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(264,plain,
! [SV30: term > $o,SV73: term] :
( ( ( ~ ( var @ SV73 )
| ( SV30 @ SV73 ) )
= $true )
| ( ( SV30 @ ( sub @ ( sK16_SY331 @ SV30 ) @ sh ) )
= $false )
| ( ( SV30 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(265,plain,
! [SV62: subst,SV50: term,SV31: term > $o] :
( ( ( ~ ( SV31 @ SV50 ) )
= $true )
| ( ( ! [SY371: term] :
( ~ ( var @ SY371 )
| ( SV31 @ ( sub @ SY371 @ ( push @ SV50 @ SV62 ) ) ) ) )
= $true )
| ( ( var @ ( sK17_SY370 @ SV50 @ SV62 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(266,plain,
! [SV62: subst,SV50: term,SV31: term > $o] :
( ( ( SV31 @ SV50 )
= $false )
| ( ( ! [SY371: term] :
( ~ ( var @ SY371 )
| ( SV31 @ ( sub @ SY371 @ ( push @ SV50 @ SV62 ) ) ) ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK17_SY370 @ SV50 @ SV62 @ SV31 ) @ SV62 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(267,plain,
! [SV34: term > $o] :
( ( ( ! [SY393: term] :
( ~ ( SV34 @ ( sK22_SY344 @ SV34 ) )
| ~ ( SV34 @ SY393 )
| ( SV34 @ ( ap @ ( sK22_SY344 @ SV34 ) @ SY393 ) ) ) )
= $false )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[253]) ).
thf(268,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK19_SY344 @ SV34 ) )
| ~ ( SV34 @ ( sK23_SY391 @ SV34 ) )
| ( SV34 @ ( ap @ ( sK19_SY344 @ SV34 ) @ ( sK23_SY391 @ SV34 ) ) ) )
= $false )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[254]) ).
thf(269,plain,
! [SV23: subst > term > term,SV70: subst > term > term] :
( ( ( ! [SY394: term,SY395: subst] :
( ( sub @ ( SV70 @ ( sK24_SY385 @ SV23 @ SV70 ) @ SY394 ) @ SY395 )
= ( SV70 @ ( comp @ ( sK24_SY385 @ SV23 @ SV70 ) @ SY395 ) @ ( sub @ SY394 @ SY395 ) ) ) )
= $false )
| ( ( ( ( lam @ ( SV23 @ sh @ one ) )
!= ( lam @ ( SV70 @ sh @ one ) ) )
| ! [SY388: subst,SY389: term] :
( ( SV23 @ SY388 @ SY389 )
= ( SV70 @ SY388 @ SY389 ) ) )
= $true )
| ( ( ( sub @ ( SV23 @ ( sK5_SY303 @ SV23 ) @ ( sK11_SY378 @ SV23 ) ) @ ( sK15_SY383 @ SV23 ) )
= ( SV23 @ ( comp @ ( sK5_SY303 @ SV23 ) @ ( sK15_SY383 @ SV23 ) ) @ ( sub @ ( sK11_SY378 @ SV23 ) @ ( sK15_SY383 @ SV23 ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[256]) ).
thf(270,plain,
! [SV24: term > $o] :
( ( ( ~ ! [SY396: term] :
( ~ ( SV24 @ SY396 )
| ( SV24 @ ( sub @ ( sK25_SY314 @ SV24 ) @ ( push @ SY396 @ id ) ) ) )
| ( SV24 @ ( lam @ ( sK25_SY314 @ SV24 ) ) ) )
= $false )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[257]) ).
thf(271,plain,
! [SV24: term > $o] :
( ( ( ! [SY314: term] :
( ~ ! [SY315: term] :
( ~ ( SV24 @ SY315 )
| ( SV24 @ ( sub @ SY314 @ ( push @ SY315 @ id ) ) ) )
| ( SV24 @ ( lam @ SY314 ) ) ) )
= $false )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(272,plain,
! [SV24: term > $o] :
( ( ( ~ ! [SY397: term] :
( ~ ( SV24 @ SY397 )
| ( SV24 @ ( sub @ ( sK26_SY314 @ SV24 ) @ ( push @ SY397 @ id ) ) ) )
| ( SV24 @ ( lam @ ( sK26_SY314 @ SV24 ) ) ) )
= $false )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[259]) ).
thf(273,plain,
! [SV29: term > $o] :
( ( ( ~ ( SV29 @ ( sK20_SY327 @ SV29 ) )
| ~ ( SV29 @ ( sK27_SY392 @ SV29 ) )
| ( SV29 @ ( ap @ ( sK20_SY327 @ SV29 ) @ ( sK27_SY392 @ SV29 ) ) ) )
= $false )
| ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[260]) ).
thf(274,plain,
! [SV29: term > $o] :
( ( ( ~ ( SV29 @ ( sK18_SY327 @ SV29 ) ) )
= $false )
| ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[261]) ).
thf(275,plain,
! [SV29: term > $o] :
( ( ( ~ ( SV29 @ ( sK21_SY390 @ SV29 ) )
| ( SV29 @ ( ap @ ( sK18_SY327 @ SV29 ) @ ( sK21_SY390 @ SV29 ) ) ) )
= $false )
| ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[261]) ).
thf(276,plain,
! [SV30: term > $o,SV72: term] :
( ( ( ~ ( var @ SV72 ) )
= $true )
| ( ( SV30 @ SV72 )
= $true )
| ( ( var @ ( sK16_SY331 @ SV30 ) )
= $true )
| ( ( SV30 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(277,plain,
! [SV30: term > $o,SV74: term] :
( ( ( ~ ( var @ SV74 )
| ( SV30 @ SV74 ) )
= $true )
| ( ( SV30 @ ( sK16_SY331 @ SV30 ) )
= $true )
| ( ( SV30 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(278,plain,
! [SV30: term > $o,SV73: term] :
( ( ( ~ ( var @ SV73 ) )
= $true )
| ( ( SV30 @ SV73 )
= $true )
| ( ( SV30 @ ( sub @ ( sK16_SY331 @ SV30 ) @ sh ) )
= $false )
| ( ( SV30 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(279,plain,
! [SV62: subst,SV50: term,SV31: term > $o] :
( ( ( SV31 @ SV50 )
= $false )
| ( ( ! [SY371: term] :
( ~ ( var @ SY371 )
| ( SV31 @ ( sub @ SY371 @ ( push @ SV50 @ SV62 ) ) ) ) )
= $true )
| ( ( var @ ( sK17_SY370 @ SV50 @ SV62 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(280,plain,
! [SV62: subst,SV50: term,SV31: term > $o,SV75: term] :
( ( ( ~ ( var @ SV75 )
| ( SV31 @ ( sub @ SV75 @ ( push @ SV50 @ SV62 ) ) ) )
= $true )
| ( ( SV31 @ SV50 )
= $false )
| ( ( SV31 @ ( sub @ ( sK17_SY370 @ SV50 @ SV62 @ SV31 ) @ SV62 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(281,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK22_SY344 @ SV34 ) )
| ~ ( SV34 @ ( sK28_SY393 @ SV34 ) )
| ( SV34 @ ( ap @ ( sK22_SY344 @ SV34 ) @ ( sK28_SY393 @ SV34 ) ) ) )
= $false )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[267]) ).
thf(282,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK19_SY344 @ SV34 ) ) )
= $false )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[268]) ).
thf(283,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK23_SY391 @ SV34 ) )
| ( SV34 @ ( ap @ ( sK19_SY344 @ SV34 ) @ ( sK23_SY391 @ SV34 ) ) ) )
= $false )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[268]) ).
thf(284,plain,
! [SV23: subst > term > term,SV70: subst > term > term] :
( ( ( ! [SY398: subst] :
( ( sub @ ( SV70 @ ( sK24_SY385 @ SV23 @ SV70 ) @ ( sK29_SY394 @ SV23 @ SV70 ) ) @ SY398 )
= ( SV70 @ ( comp @ ( sK24_SY385 @ SV23 @ SV70 ) @ SY398 ) @ ( sub @ ( sK29_SY394 @ SV23 @ SV70 ) @ SY398 ) ) ) )
= $false )
| ( ( ( ( lam @ ( SV23 @ sh @ one ) )
!= ( lam @ ( SV70 @ sh @ one ) ) )
| ! [SY388: subst,SY389: term] :
( ( SV23 @ SY388 @ SY389 )
= ( SV70 @ SY388 @ SY389 ) ) )
= $true )
| ( ( ( sub @ ( SV23 @ ( sK5_SY303 @ SV23 ) @ ( sK11_SY378 @ SV23 ) ) @ ( sK15_SY383 @ SV23 ) )
= ( SV23 @ ( comp @ ( sK5_SY303 @ SV23 ) @ ( sK15_SY383 @ SV23 ) ) @ ( sub @ ( sK11_SY378 @ SV23 ) @ ( sK15_SY383 @ SV23 ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[269]) ).
thf(285,plain,
! [SV24: term > $o] :
( ( ( ~ ! [SY396: term] :
( ~ ( SV24 @ SY396 )
| ( SV24 @ ( sub @ ( sK25_SY314 @ SV24 ) @ ( push @ SY396 @ id ) ) ) ) )
= $false )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[270]) ).
thf(286,plain,
! [SV24: term > $o] :
( ( ( SV24 @ ( lam @ ( sK25_SY314 @ SV24 ) ) )
= $false )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[270]) ).
thf(287,plain,
! [SV24: term > $o] :
( ( ( ~ ! [SY399: term] :
( ~ ( SV24 @ SY399 )
| ( SV24 @ ( sub @ ( sK30_SY314 @ SV24 ) @ ( push @ SY399 @ id ) ) ) )
| ( SV24 @ ( lam @ ( sK30_SY314 @ SV24 ) ) ) )
= $false )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[271]) ).
thf(288,plain,
! [SV24: term > $o] :
( ( ( ~ ! [SY397: term] :
( ~ ( SV24 @ SY397 )
| ( SV24 @ ( sub @ ( sK26_SY314 @ SV24 ) @ ( push @ SY397 @ id ) ) ) ) )
= $false )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[272]) ).
thf(289,plain,
! [SV24: term > $o] :
( ( ( SV24 @ ( lam @ ( sK26_SY314 @ SV24 ) ) )
= $false )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[272]) ).
thf(290,plain,
! [SV29: term > $o] :
( ( ( ~ ( SV29 @ ( sK20_SY327 @ SV29 ) ) )
= $false )
| ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(291,plain,
! [SV29: term > $o] :
( ( ( ~ ( SV29 @ ( sK27_SY392 @ SV29 ) )
| ( SV29 @ ( ap @ ( sK20_SY327 @ SV29 ) @ ( sK27_SY392 @ SV29 ) ) ) )
= $false )
| ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(292,plain,
! [SV29: term > $o] :
( ( ( SV29 @ ( sK18_SY327 @ SV29 ) )
= $true )
| ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(293,plain,
! [SV29: term > $o] :
( ( ( ~ ( SV29 @ ( sK21_SY390 @ SV29 ) ) )
= $false )
| ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[275]) ).
thf(294,plain,
! [SV29: term > $o] :
( ( ( SV29 @ ( ap @ ( sK18_SY327 @ SV29 ) @ ( sK21_SY390 @ SV29 ) ) )
= $false )
| ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[275]) ).
thf(295,plain,
! [SV30: term > $o,SV72: term] :
( ( ( var @ SV72 )
= $false )
| ( ( SV30 @ SV72 )
= $true )
| ( ( var @ ( sK16_SY331 @ SV30 ) )
= $true )
| ( ( SV30 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(296,plain,
! [SV30: term > $o,SV74: term] :
( ( ( ~ ( var @ SV74 ) )
= $true )
| ( ( SV30 @ SV74 )
= $true )
| ( ( SV30 @ ( sK16_SY331 @ SV30 ) )
= $true )
| ( ( SV30 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(297,plain,
! [SV30: term > $o,SV73: term] :
( ( ( var @ SV73 )
= $false )
| ( ( SV30 @ SV73 )
= $true )
| ( ( SV30 @ ( sub @ ( sK16_SY331 @ SV30 ) @ sh ) )
= $false )
| ( ( SV30 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(298,plain,
! [SV62: subst,SV50: term,SV31: term > $o,SV76: term] :
( ( ( ~ ( var @ SV76 )
| ( SV31 @ ( sub @ SV76 @ ( push @ SV50 @ SV62 ) ) ) )
= $true )
| ( ( SV31 @ SV50 )
= $false )
| ( ( var @ ( sK17_SY370 @ SV50 @ SV62 @ SV31 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(299,plain,
! [SV62: subst,SV50: term,SV31: term > $o,SV75: term] :
( ( ( ~ ( var @ SV75 ) )
= $true )
| ( ( SV31 @ ( sub @ SV75 @ ( push @ SV50 @ SV62 ) ) )
= $true )
| ( ( SV31 @ SV50 )
= $false )
| ( ( SV31 @ ( sub @ ( sK17_SY370 @ SV50 @ SV62 @ SV31 ) @ SV62 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(300,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK22_SY344 @ SV34 ) ) )
= $false )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(301,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK28_SY393 @ SV34 ) )
| ( SV34 @ ( ap @ ( sK22_SY344 @ SV34 ) @ ( sK28_SY393 @ SV34 ) ) ) )
= $false )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(302,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( sK19_SY344 @ SV34 ) )
= $true )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(303,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK23_SY391 @ SV34 ) ) )
= $false )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[283]) ).
thf(304,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( ap @ ( sK19_SY344 @ SV34 ) @ ( sK23_SY391 @ SV34 ) ) )
= $false )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[283]) ).
thf(305,plain,
! [SV23: subst > term > term,SV70: subst > term > term] :
( ( ( ( sub @ ( SV70 @ ( sK24_SY385 @ SV23 @ SV70 ) @ ( sK29_SY394 @ SV23 @ SV70 ) ) @ ( sK31_SY398 @ SV23 @ SV70 ) )
= ( SV70 @ ( comp @ ( sK24_SY385 @ SV23 @ SV70 ) @ ( sK31_SY398 @ SV23 @ SV70 ) ) @ ( sub @ ( sK29_SY394 @ SV23 @ SV70 ) @ ( sK31_SY398 @ SV23 @ SV70 ) ) ) )
= $false )
| ( ( ( ( lam @ ( SV23 @ sh @ one ) )
!= ( lam @ ( SV70 @ sh @ one ) ) )
| ! [SY388: subst,SY389: term] :
( ( SV23 @ SY388 @ SY389 )
= ( SV70 @ SY388 @ SY389 ) ) )
= $true )
| ( ( ( sub @ ( SV23 @ ( sK5_SY303 @ SV23 ) @ ( sK11_SY378 @ SV23 ) ) @ ( sK15_SY383 @ SV23 ) )
= ( SV23 @ ( comp @ ( sK5_SY303 @ SV23 ) @ ( sK15_SY383 @ SV23 ) ) @ ( sub @ ( sK11_SY378 @ SV23 ) @ ( sK15_SY383 @ SV23 ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[284]) ).
thf(306,plain,
! [SV24: term > $o] :
( ( ( ! [SY396: term] :
( ~ ( SV24 @ SY396 )
| ( SV24 @ ( sub @ ( sK25_SY314 @ SV24 ) @ ( push @ SY396 @ id ) ) ) ) )
= $true )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(307,plain,
! [SV77: term,SV24: term > $o] :
( ( ( ! [SY400: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY400 ) ) )
| ( SV24 @ ( sub @ SV77 @ SY400 ) ) ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK25_SY314 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(308,plain,
! [SV24: term > $o] :
( ( ( ~ ! [SY399: term] :
( ~ ( SV24 @ SY399 )
| ( SV24 @ ( sub @ ( sK30_SY314 @ SV24 ) @ ( push @ SY399 @ id ) ) ) ) )
= $false )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[287]) ).
thf(309,plain,
! [SV24: term > $o] :
( ( ( SV24 @ ( lam @ ( sK30_SY314 @ SV24 ) ) )
= $false )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[287]) ).
thf(310,plain,
! [SV24: term > $o] :
( ( ( ! [SY397: term] :
( ~ ( SV24 @ SY397 )
| ( SV24 @ ( sub @ ( sK26_SY314 @ SV24 ) @ ( push @ SY397 @ id ) ) ) ) )
= $true )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(311,plain,
! [SV78: term,SV24: term > $o] :
( ( ( ! [SY402: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY402 ) ) )
| ( SV24 @ ( sub @ SV78 @ SY402 ) ) ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK26_SY314 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(312,plain,
! [SV29: term > $o] :
( ( ( SV29 @ ( sK20_SY327 @ SV29 ) )
= $true )
| ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[290]) ).
thf(313,plain,
! [SV29: term > $o] :
( ( ( ~ ( SV29 @ ( sK27_SY392 @ SV29 ) ) )
= $false )
| ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(314,plain,
! [SV29: term > $o] :
( ( ( SV29 @ ( ap @ ( sK20_SY327 @ SV29 ) @ ( sK27_SY392 @ SV29 ) ) )
= $false )
| ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(315,plain,
! [SV29: term > $o] :
( ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) ) )
= $true )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK18_SY327 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(316,plain,
! [SV29: term > $o] :
( ( ( SV29 @ ( sK21_SY390 @ SV29 ) )
= $true )
| ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(317,plain,
! [SV29: term > $o] :
( ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) ) )
= $true )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( ap @ ( sK18_SY327 @ SV29 ) @ ( sK21_SY390 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(318,plain,
! [SV30: term > $o,SV74: term] :
( ( ( var @ SV74 )
= $false )
| ( ( SV30 @ SV74 )
= $true )
| ( ( SV30 @ ( sK16_SY331 @ SV30 ) )
= $true )
| ( ( SV30 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(319,plain,
! [SV62: subst,SV50: term,SV31: term > $o,SV76: term] :
( ( ( ~ ( var @ SV76 ) )
= $true )
| ( ( SV31 @ ( sub @ SV76 @ ( push @ SV50 @ SV62 ) ) )
= $true )
| ( ( SV31 @ SV50 )
= $false )
| ( ( var @ ( sK17_SY370 @ SV50 @ SV62 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(320,plain,
! [SV62: subst,SV50: term,SV31: term > $o,SV75: term] :
( ( ( var @ SV75 )
= $false )
| ( ( SV31 @ ( sub @ SV75 @ ( push @ SV50 @ SV62 ) ) )
= $true )
| ( ( SV31 @ SV50 )
= $false )
| ( ( SV31 @ ( sub @ ( sK17_SY370 @ SV50 @ SV62 @ SV31 ) @ SV62 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(321,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( sK22_SY344 @ SV34 ) )
= $true )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(322,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK28_SY393 @ SV34 ) ) )
= $false )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[301]) ).
thf(323,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( ap @ ( sK22_SY344 @ SV34 ) @ ( sK28_SY393 @ SV34 ) ) )
= $false )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[301]) ).
thf(324,plain,
! [SV34: term > $o] :
( ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK19_SY344 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(325,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( sK23_SY391 @ SV34 ) )
= $true )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[303]) ).
thf(326,plain,
! [SV34: term > $o] :
( ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK19_SY344 @ SV34 ) @ ( sK23_SY391 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(327,plain,
! [SV70: subst > term > term,SV23: subst > term > term] :
( ( ( ( lam @ ( SV23 @ sh @ one ) )
!= ( lam @ ( SV70 @ sh @ one ) ) )
= $true )
| ( ( ! [SY388: subst,SY389: term] :
( ( SV23 @ SY388 @ SY389 )
= ( SV70 @ SY388 @ SY389 ) ) )
= $true )
| ( ( ( sub @ ( SV70 @ ( sK24_SY385 @ SV23 @ SV70 ) @ ( sK29_SY394 @ SV23 @ SV70 ) ) @ ( sK31_SY398 @ SV23 @ SV70 ) )
= ( SV70 @ ( comp @ ( sK24_SY385 @ SV23 @ SV70 ) @ ( sK31_SY398 @ SV23 @ SV70 ) ) @ ( sub @ ( sK29_SY394 @ SV23 @ SV70 ) @ ( sK31_SY398 @ SV23 @ SV70 ) ) ) )
= $false )
| ( ( ( sub @ ( SV23 @ ( sK5_SY303 @ SV23 ) @ ( sK11_SY378 @ SV23 ) ) @ ( sK15_SY383 @ SV23 ) )
= ( SV23 @ ( comp @ ( sK5_SY303 @ SV23 ) @ ( sK15_SY383 @ SV23 ) ) @ ( sub @ ( sK11_SY378 @ SV23 ) @ ( sK15_SY383 @ SV23 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(328,plain,
! [SV79: term,SV24: term > $o] :
( ( ( ~ ( SV24 @ SV79 )
| ( SV24 @ ( sub @ ( sK25_SY314 @ SV24 ) @ ( push @ SV79 @ id ) ) ) )
= $true )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(329,plain,
! [SV77: term,SV80: subst,SV24: term > $o] :
( ( ( ~ ! [SY404: term] :
( ~ ( var @ SY404 )
| ( SV24 @ ( sub @ SY404 @ SV80 ) ) )
| ( SV24 @ ( sub @ SV77 @ SV80 ) ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK25_SY314 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(330,plain,
! [SV24: term > $o] :
( ( ( ! [SY399: term] :
( ~ ( SV24 @ SY399 )
| ( SV24 @ ( sub @ ( sK30_SY314 @ SV24 ) @ ( push @ SY399 @ id ) ) ) ) )
= $true )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(331,plain,
! [SV81: term,SV24: term > $o] :
( ( ( ! [SY405: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY405 ) ) )
| ( SV24 @ ( sub @ SV81 @ SY405 ) ) ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK30_SY314 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(332,plain,
! [SV82: term,SV24: term > $o] :
( ( ( ~ ( SV24 @ SV82 )
| ( SV24 @ ( sub @ ( sK26_SY314 @ SV24 ) @ ( push @ SV82 @ id ) ) ) )
= $true )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(333,plain,
! [SV78: term,SV83: subst,SV24: term > $o] :
( ( ( ~ ! [SY407: term] :
( ~ ( var @ SY407 )
| ( SV24 @ ( sub @ SY407 @ SV83 ) ) )
| ( SV24 @ ( sub @ SV78 @ SV83 ) ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK26_SY314 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(334,plain,
! [SV29: term > $o] :
( ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) ) )
= $true )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK20_SY327 @ SV29 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(335,plain,
! [SV29: term > $o] :
( ( ( SV29 @ ( sK27_SY392 @ SV29 ) )
= $true )
| ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) )
| ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[313]) ).
thf(336,plain,
! [SV29: term > $o] :
( ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) ) )
= $true )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( ap @ ( sK20_SY327 @ SV29 ) @ ( sK27_SY392 @ SV29 ) ) )
= $false )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(337,plain,
! [SV29: term > $o] :
( ( ( ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) ) )
= $false )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK18_SY327 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(338,plain,
! [SV29: term > $o] :
( ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) ) )
= $true )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK21_SY390 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(339,plain,
! [SV29: term > $o] :
( ( ( ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) ) )
= $false )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( ap @ ( sK18_SY327 @ SV29 ) @ ( sK21_SY390 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(340,plain,
! [SV62: subst,SV50: term,SV31: term > $o,SV76: term] :
( ( ( var @ SV76 )
= $false )
| ( ( SV31 @ ( sub @ SV76 @ ( push @ SV50 @ SV62 ) ) )
= $true )
| ( ( SV31 @ SV50 )
= $false )
| ( ( var @ ( sK17_SY370 @ SV50 @ SV62 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(341,plain,
! [SV34: term > $o] :
( ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK22_SY344 @ SV34 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(342,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( sK28_SY393 @ SV34 ) )
= $true )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) )
| ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[322]) ).
thf(343,plain,
! [SV34: term > $o] :
( ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK22_SY344 @ SV34 ) @ ( sK28_SY393 @ SV34 ) ) )
= $false )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(344,plain,
! [SV34: term > $o] :
( ( ( ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) ) )
= $false )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK19_SY344 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(345,plain,
! [SV34: term > $o] :
( ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK23_SY391 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(346,plain,
! [SV34: term > $o] :
( ( ( ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) ) )
= $false )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK19_SY344 @ SV34 ) @ ( sK23_SY391 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(347,plain,
! [SV70: subst > term > term,SV23: subst > term > term] :
( ( ( ( lam @ ( SV23 @ sh @ one ) )
= ( lam @ ( SV70 @ sh @ one ) ) )
= $false )
| ( ( ! [SY388: subst,SY389: term] :
( ( SV23 @ SY388 @ SY389 )
= ( SV70 @ SY388 @ SY389 ) ) )
= $true )
| ( ( ( sub @ ( SV70 @ ( sK24_SY385 @ SV23 @ SV70 ) @ ( sK29_SY394 @ SV23 @ SV70 ) ) @ ( sK31_SY398 @ SV23 @ SV70 ) )
= ( SV70 @ ( comp @ ( sK24_SY385 @ SV23 @ SV70 ) @ ( sK31_SY398 @ SV23 @ SV70 ) ) @ ( sub @ ( sK29_SY394 @ SV23 @ SV70 ) @ ( sK31_SY398 @ SV23 @ SV70 ) ) ) )
= $false )
| ( ( ( sub @ ( SV23 @ ( sK5_SY303 @ SV23 ) @ ( sK11_SY378 @ SV23 ) ) @ ( sK15_SY383 @ SV23 ) )
= ( SV23 @ ( comp @ ( sK5_SY303 @ SV23 ) @ ( sK15_SY383 @ SV23 ) ) @ ( sub @ ( sK11_SY378 @ SV23 ) @ ( sK15_SY383 @ SV23 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(348,plain,
! [SV79: term,SV24: term > $o] :
( ( ( ~ ( SV24 @ SV79 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK25_SY314 @ SV24 ) @ ( push @ SV79 @ id ) ) )
= $true )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(349,plain,
! [SV77: term,SV80: subst,SV24: term > $o] :
( ( ( ~ ! [SY404: term] :
( ~ ( var @ SY404 )
| ( SV24 @ ( sub @ SY404 @ SV80 ) ) ) )
= $true )
| ( ( SV24 @ ( sub @ SV77 @ SV80 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK25_SY314 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(350,plain,
! [SV84: term,SV24: term > $o] :
( ( ( ~ ( SV24 @ SV84 )
| ( SV24 @ ( sub @ ( sK30_SY314 @ SV24 ) @ ( push @ SV84 @ id ) ) ) )
= $true )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(351,plain,
! [SV81: term,SV85: subst,SV24: term > $o] :
( ( ( ~ ! [SY408: term] :
( ~ ( var @ SY408 )
| ( SV24 @ ( sub @ SY408 @ SV85 ) ) )
| ( SV24 @ ( sub @ SV81 @ SV85 ) ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK30_SY314 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(352,plain,
! [SV82: term,SV24: term > $o] :
( ( ( ~ ( SV24 @ SV82 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK26_SY314 @ SV24 ) @ ( push @ SV82 @ id ) ) )
= $true )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(353,plain,
! [SV78: term,SV83: subst,SV24: term > $o] :
( ( ( ~ ! [SY407: term] :
( ~ ( var @ SY407 )
| ( SV24 @ ( sub @ SY407 @ SV83 ) ) ) )
= $true )
| ( ( SV24 @ ( sub @ SV78 @ SV83 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK26_SY314 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(354,plain,
! [SV29: term > $o] :
( ( ( ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) ) )
= $false )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK20_SY327 @ SV29 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(355,plain,
! [SV29: term > $o] :
( ( ( ~ ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) ) )
= $true )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK27_SY392 @ SV29 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(356,plain,
! [SV29: term > $o] :
( ( ( ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) ) )
= $false )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( ap @ ( sK20_SY327 @ SV29 ) @ ( sK27_SY392 @ SV29 ) ) )
= $false )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(357,plain,
! [SV29: term > $o] :
( ( ( ~ ( SV29 @ ( sK32_SY329 @ SV29 ) )
| ( SV29 @ ( lam @ ( sK32_SY329 @ SV29 ) ) ) )
= $false )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK18_SY327 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[337]) ).
thf(358,plain,
! [SV29: term > $o] :
( ( ( ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) ) )
= $false )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK21_SY390 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(359,plain,
! [SV29: term > $o] :
( ( ( ~ ( SV29 @ ( sK33_SY329 @ SV29 ) )
| ( SV29 @ ( lam @ ( sK33_SY329 @ SV29 ) ) ) )
= $false )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( ap @ ( sK18_SY327 @ SV29 ) @ ( sK21_SY390 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[339]) ).
thf(360,plain,
! [SV34: term > $o] :
( ( ( ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) ) )
= $false )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK22_SY344 @ SV34 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(361,plain,
! [SV34: term > $o] :
( ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK28_SY393 @ SV34 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(362,plain,
! [SV34: term > $o] :
( ( ( ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) ) )
= $false )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK22_SY344 @ SV34 ) @ ( sK28_SY393 @ SV34 ) ) )
= $false )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(363,plain,
! [SV34: term > $o] :
( ( ( ~ ! [SY409: term] :
( ~ ( SV34 @ SY409 )
| ( SV34 @ ( sub @ ( sK34_SY346 @ SV34 ) @ ( push @ SY409 @ id ) ) ) )
| ( SV34 @ ( lam @ ( sK34_SY346 @ SV34 ) ) ) )
= $false )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK19_SY344 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[344]) ).
thf(364,plain,
! [SV34: term > $o] :
( ( ( ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) ) )
= $false )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK23_SY391 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(365,plain,
! [SV34: term > $o] :
( ( ( ~ ! [SY410: term] :
( ~ ( SV34 @ SY410 )
| ( SV34 @ ( sub @ ( sK35_SY346 @ SV34 ) @ ( push @ SY410 @ id ) ) ) )
| ( SV34 @ ( lam @ ( sK35_SY346 @ SV34 ) ) ) )
= $false )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK19_SY344 @ SV34 ) @ ( sK23_SY391 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[346]) ).
thf(366,plain,
! [SV70: subst > term > term,SV86: subst,SV23: subst > term > term] :
( ( ( ! [SY411: term] :
( ( SV23 @ SV86 @ SY411 )
= ( SV70 @ SV86 @ SY411 ) ) )
= $true )
| ( ( ( lam @ ( SV23 @ sh @ one ) )
= ( lam @ ( SV70 @ sh @ one ) ) )
= $false )
| ( ( ( sub @ ( SV70 @ ( sK24_SY385 @ SV23 @ SV70 ) @ ( sK29_SY394 @ SV23 @ SV70 ) ) @ ( sK31_SY398 @ SV23 @ SV70 ) )
= ( SV70 @ ( comp @ ( sK24_SY385 @ SV23 @ SV70 ) @ ( sK31_SY398 @ SV23 @ SV70 ) ) @ ( sub @ ( sK29_SY394 @ SV23 @ SV70 ) @ ( sK31_SY398 @ SV23 @ SV70 ) ) ) )
= $false )
| ( ( ( sub @ ( SV23 @ ( sK5_SY303 @ SV23 ) @ ( sK11_SY378 @ SV23 ) ) @ ( sK15_SY383 @ SV23 ) )
= ( SV23 @ ( comp @ ( sK5_SY303 @ SV23 ) @ ( sK15_SY383 @ SV23 ) ) @ ( sub @ ( sK11_SY378 @ SV23 ) @ ( sK15_SY383 @ SV23 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(367,plain,
! [SV79: term,SV24: term > $o] :
( ( ( SV24 @ SV79 )
= $false )
| ( ( SV24 @ ( sub @ ( sK25_SY314 @ SV24 ) @ ( push @ SV79 @ id ) ) )
= $true )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(368,plain,
! [SV77: term,SV80: subst,SV24: term > $o] :
( ( ( ! [SY404: term] :
( ~ ( var @ SY404 )
| ( SV24 @ ( sub @ SY404 @ SV80 ) ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV77 @ SV80 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK25_SY314 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(369,plain,
! [SV84: term,SV24: term > $o] :
( ( ( ~ ( SV24 @ SV84 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK30_SY314 @ SV24 ) @ ( push @ SV84 @ id ) ) )
= $true )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(370,plain,
! [SV81: term,SV85: subst,SV24: term > $o] :
( ( ( ~ ! [SY408: term] :
( ~ ( var @ SY408 )
| ( SV24 @ ( sub @ SY408 @ SV85 ) ) ) )
= $true )
| ( ( SV24 @ ( sub @ SV81 @ SV85 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK30_SY314 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(371,plain,
! [SV82: term,SV24: term > $o] :
( ( ( SV24 @ SV82 )
= $false )
| ( ( SV24 @ ( sub @ ( sK26_SY314 @ SV24 ) @ ( push @ SV82 @ id ) ) )
= $true )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(372,plain,
! [SV78: term,SV83: subst,SV24: term > $o] :
( ( ( ! [SY407: term] :
( ~ ( var @ SY407 )
| ( SV24 @ ( sub @ SY407 @ SV83 ) ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV78 @ SV83 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK26_SY314 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(373,plain,
! [SV29: term > $o] :
( ( ( ~ ( SV29 @ ( sK36_SY329 @ SV29 ) )
| ( SV29 @ ( lam @ ( sK36_SY329 @ SV29 ) ) ) )
= $false )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK20_SY327 @ SV29 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[354]) ).
thf(374,plain,
! [SV29: term > $o] :
( ( ( ! [SY329: term] :
( ~ ( SV29 @ SY329 )
| ( SV29 @ ( lam @ SY329 ) ) ) )
= $false )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK27_SY392 @ SV29 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(375,plain,
! [SV29: term > $o] :
( ( ( ~ ( SV29 @ ( sK37_SY329 @ SV29 ) )
| ( SV29 @ ( lam @ ( sK37_SY329 @ SV29 ) ) ) )
= $false )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( ap @ ( sK20_SY327 @ SV29 ) @ ( sK27_SY392 @ SV29 ) ) )
= $false )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[356]) ).
thf(376,plain,
! [SV29: term > $o] :
( ( ( ~ ( SV29 @ ( sK32_SY329 @ SV29 ) ) )
= $false )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK18_SY327 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[357]) ).
thf(377,plain,
! [SV29: term > $o] :
( ( ( SV29 @ ( lam @ ( sK32_SY329 @ SV29 ) ) )
= $false )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK18_SY327 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[357]) ).
thf(378,plain,
! [SV29: term > $o] :
( ( ( ~ ( SV29 @ ( sK38_SY329 @ SV29 ) )
| ( SV29 @ ( lam @ ( sK38_SY329 @ SV29 ) ) ) )
= $false )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK21_SY390 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[358]) ).
thf(379,plain,
! [SV29: term > $o] :
( ( ( ~ ( SV29 @ ( sK33_SY329 @ SV29 ) ) )
= $false )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( ap @ ( sK18_SY327 @ SV29 ) @ ( sK21_SY390 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(380,plain,
! [SV29: term > $o] :
( ( ( SV29 @ ( lam @ ( sK33_SY329 @ SV29 ) ) )
= $false )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( ap @ ( sK18_SY327 @ SV29 ) @ ( sK21_SY390 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(381,plain,
! [SV34: term > $o] :
( ( ( ~ ! [SY412: term] :
( ~ ( SV34 @ SY412 )
| ( SV34 @ ( sub @ ( sK39_SY346 @ SV34 ) @ ( push @ SY412 @ id ) ) ) )
| ( SV34 @ ( lam @ ( sK39_SY346 @ SV34 ) ) ) )
= $false )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK22_SY344 @ SV34 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[360]) ).
thf(382,plain,
! [SV34: term > $o] :
( ( ( ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV34 @ SY347 )
| ( SV34 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV34 @ ( lam @ SY346 ) ) ) )
= $false )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK28_SY393 @ SV34 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(383,plain,
! [SV34: term > $o] :
( ( ( ~ ! [SY413: term] :
( ~ ( SV34 @ SY413 )
| ( SV34 @ ( sub @ ( sK40_SY346 @ SV34 ) @ ( push @ SY413 @ id ) ) ) )
| ( SV34 @ ( lam @ ( sK40_SY346 @ SV34 ) ) ) )
= $false )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK22_SY344 @ SV34 ) @ ( sK28_SY393 @ SV34 ) ) )
= $false )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[362]) ).
thf(384,plain,
! [SV34: term > $o] :
( ( ( ~ ! [SY409: term] :
( ~ ( SV34 @ SY409 )
| ( SV34 @ ( sub @ ( sK34_SY346 @ SV34 ) @ ( push @ SY409 @ id ) ) ) ) )
= $false )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK19_SY344 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[363]) ).
thf(385,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( lam @ ( sK34_SY346 @ SV34 ) ) )
= $false )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK19_SY344 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[363]) ).
thf(386,plain,
! [SV34: term > $o] :
( ( ( ~ ! [SY414: term] :
( ~ ( SV34 @ SY414 )
| ( SV34 @ ( sub @ ( sK41_SY346 @ SV34 ) @ ( push @ SY414 @ id ) ) ) )
| ( SV34 @ ( lam @ ( sK41_SY346 @ SV34 ) ) ) )
= $false )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK23_SY391 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[364]) ).
thf(387,plain,
! [SV34: term > $o] :
( ( ( ~ ! [SY410: term] :
( ~ ( SV34 @ SY410 )
| ( SV34 @ ( sub @ ( sK35_SY346 @ SV34 ) @ ( push @ SY410 @ id ) ) ) ) )
= $false )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK19_SY344 @ SV34 ) @ ( sK23_SY391 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[365]) ).
thf(388,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( lam @ ( sK35_SY346 @ SV34 ) ) )
= $false )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK19_SY344 @ SV34 ) @ ( sK23_SY391 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[365]) ).
thf(389,plain,
! [SV70: subst > term > term,SV87: term,SV86: subst,SV23: subst > term > term] :
( ( ( ( SV23 @ SV86 @ SV87 )
= ( SV70 @ SV86 @ SV87 ) )
= $true )
| ( ( ( lam @ ( SV23 @ sh @ one ) )
= ( lam @ ( SV70 @ sh @ one ) ) )
= $false )
| ( ( ( sub @ ( SV70 @ ( sK24_SY385 @ SV23 @ SV70 ) @ ( sK29_SY394 @ SV23 @ SV70 ) ) @ ( sK31_SY398 @ SV23 @ SV70 ) )
= ( SV70 @ ( comp @ ( sK24_SY385 @ SV23 @ SV70 ) @ ( sK31_SY398 @ SV23 @ SV70 ) ) @ ( sub @ ( sK29_SY394 @ SV23 @ SV70 ) @ ( sK31_SY398 @ SV23 @ SV70 ) ) ) )
= $false )
| ( ( ( sub @ ( SV23 @ ( sK5_SY303 @ SV23 ) @ ( sK11_SY378 @ SV23 ) ) @ ( sK15_SY383 @ SV23 ) )
= ( SV23 @ ( comp @ ( sK5_SY303 @ SV23 ) @ ( sK15_SY383 @ SV23 ) ) @ ( sub @ ( sK11_SY378 @ SV23 ) @ ( sK15_SY383 @ SV23 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(390,plain,
! [SV79: term,SV88: term,SV24: term > $o] :
( ( ( ! [SY415: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY415 ) ) )
| ( SV24 @ ( sub @ SV88 @ SY415 ) ) ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK25_SY314 @ SV24 ) @ ( push @ SV79 @ id ) ) )
= $true )
| ( ( SV24 @ SV79 )
= $false )
| ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(391,plain,
! [SV24: term > $o,SV80: subst,SV77: term] :
( ( ( ~ ( var @ ( sK42_SY404 @ SV77 @ SV80 @ SV24 ) )
| ( SV24 @ ( sub @ ( sK42_SY404 @ SV77 @ SV80 @ SV24 ) @ SV80 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV77 @ SV80 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK25_SY314 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[368]) ).
thf(392,plain,
! [SV84: term,SV24: term > $o] :
( ( ( SV24 @ SV84 )
= $false )
| ( ( SV24 @ ( sub @ ( sK30_SY314 @ SV24 ) @ ( push @ SV84 @ id ) ) )
= $true )
| ( ( ! [SY316: term,SY317: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY317 ) ) )
| ( SV24 @ ( sub @ SY316 @ SY317 ) ) ) )
= $true )
| ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(393,plain,
! [SV81: term,SV85: subst,SV24: term > $o] :
( ( ( ! [SY408: term] :
( ~ ( var @ SY408 )
| ( SV24 @ ( sub @ SY408 @ SV85 ) ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV81 @ SV85 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK30_SY314 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(394,plain,
! [SV82: term,SV89: term,SV24: term > $o] :
( ( ( ! [SY417: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY417 ) ) )
| ( SV24 @ ( sub @ SV89 @ SY417 ) ) ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK26_SY314 @ SV24 ) @ ( push @ SV82 @ id ) ) )
= $true )
| ( ( SV24 @ SV82 )
= $false )
| ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(395,plain,
! [SV24: term > $o,SV83: subst,SV78: term] :
( ( ( ~ ( var @ ( sK43_SY407 @ SV78 @ SV83 @ SV24 ) )
| ( SV24 @ ( sub @ ( sK43_SY407 @ SV78 @ SV83 @ SV24 ) @ SV83 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV78 @ SV83 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK26_SY314 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[372]) ).
thf(396,plain,
! [SV29: term > $o] :
( ( ( ~ ( SV29 @ ( sK36_SY329 @ SV29 ) ) )
= $false )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK20_SY327 @ SV29 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[373]) ).
thf(397,plain,
! [SV29: term > $o] :
( ( ( SV29 @ ( lam @ ( sK36_SY329 @ SV29 ) ) )
= $false )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK20_SY327 @ SV29 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[373]) ).
thf(398,plain,
! [SV29: term > $o] :
( ( ( ~ ( SV29 @ ( sK44_SY329 @ SV29 ) )
| ( SV29 @ ( lam @ ( sK44_SY329 @ SV29 ) ) ) )
= $false )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK27_SY392 @ SV29 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[374]) ).
thf(399,plain,
! [SV29: term > $o] :
( ( ( ~ ( SV29 @ ( sK37_SY329 @ SV29 ) ) )
= $false )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( ap @ ( sK20_SY327 @ SV29 ) @ ( sK27_SY392 @ SV29 ) ) )
= $false )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[375]) ).
thf(400,plain,
! [SV29: term > $o] :
( ( ( SV29 @ ( lam @ ( sK37_SY329 @ SV29 ) ) )
= $false )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( ap @ ( sK20_SY327 @ SV29 ) @ ( sK27_SY392 @ SV29 ) ) )
= $false )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[375]) ).
thf(401,plain,
! [SV29: term > $o] :
( ( ( SV29 @ ( sK32_SY329 @ SV29 ) )
= $true )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK18_SY327 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[376]) ).
thf(402,plain,
! [SV90: term,SV29: term > $o] :
( ( ( SV29 @ SV90 )
= $true )
| ( ( SV29 @ ( lam @ ( sK32_SY329 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK18_SY327 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(403,plain,
! [SV29: term > $o] :
( ( ( ~ ( SV29 @ ( sK38_SY329 @ SV29 ) ) )
= $false )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK21_SY390 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[378]) ).
thf(404,plain,
! [SV29: term > $o] :
( ( ( SV29 @ ( lam @ ( sK38_SY329 @ SV29 ) ) )
= $false )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK21_SY390 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[378]) ).
thf(405,plain,
! [SV29: term > $o] :
( ( ( SV29 @ ( sK33_SY329 @ SV29 ) )
= $true )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( ap @ ( sK18_SY327 @ SV29 ) @ ( sK21_SY390 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[379]) ).
thf(406,plain,
! [SV91: term,SV29: term > $o] :
( ( ( SV29 @ SV91 )
= $true )
| ( ( SV29 @ ( lam @ ( sK33_SY329 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( ap @ ( sK18_SY327 @ SV29 ) @ ( sK21_SY390 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(407,plain,
! [SV34: term > $o] :
( ( ( ~ ! [SY412: term] :
( ~ ( SV34 @ SY412 )
| ( SV34 @ ( sub @ ( sK39_SY346 @ SV34 ) @ ( push @ SY412 @ id ) ) ) ) )
= $false )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK22_SY344 @ SV34 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[381]) ).
thf(408,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( lam @ ( sK39_SY346 @ SV34 ) ) )
= $false )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK22_SY344 @ SV34 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[381]) ).
thf(409,plain,
! [SV34: term > $o] :
( ( ( ~ ! [SY419: term] :
( ~ ( SV34 @ SY419 )
| ( SV34 @ ( sub @ ( sK45_SY346 @ SV34 ) @ ( push @ SY419 @ id ) ) ) )
| ( SV34 @ ( lam @ ( sK45_SY346 @ SV34 ) ) ) )
= $false )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK28_SY393 @ SV34 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[382]) ).
thf(410,plain,
! [SV34: term > $o] :
( ( ( ~ ! [SY413: term] :
( ~ ( SV34 @ SY413 )
| ( SV34 @ ( sub @ ( sK40_SY346 @ SV34 ) @ ( push @ SY413 @ id ) ) ) ) )
= $false )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK22_SY344 @ SV34 ) @ ( sK28_SY393 @ SV34 ) ) )
= $false )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[383]) ).
thf(411,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( lam @ ( sK40_SY346 @ SV34 ) ) )
= $false )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK22_SY344 @ SV34 ) @ ( sK28_SY393 @ SV34 ) ) )
= $false )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[383]) ).
thf(412,plain,
! [SV34: term > $o] :
( ( ( ! [SY409: term] :
( ~ ( SV34 @ SY409 )
| ( SV34 @ ( sub @ ( sK34_SY346 @ SV34 ) @ ( push @ SY409 @ id ) ) ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK19_SY344 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[384]) ).
thf(413,plain,
! [SV92: term,SV34: term > $o] :
( ( ( SV34 @ SV92 )
= $true )
| ( ( SV34 @ ( lam @ ( sK34_SY346 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK19_SY344 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(414,plain,
! [SV34: term > $o] :
( ( ( ~ ! [SY414: term] :
( ~ ( SV34 @ SY414 )
| ( SV34 @ ( sub @ ( sK41_SY346 @ SV34 ) @ ( push @ SY414 @ id ) ) ) ) )
= $false )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK23_SY391 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[386]) ).
thf(415,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( lam @ ( sK41_SY346 @ SV34 ) ) )
= $false )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK23_SY391 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[386]) ).
thf(416,plain,
! [SV34: term > $o] :
( ( ( ! [SY410: term] :
( ~ ( SV34 @ SY410 )
| ( SV34 @ ( sub @ ( sK35_SY346 @ SV34 ) @ ( push @ SY410 @ id ) ) ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK19_SY344 @ SV34 ) @ ( sK23_SY391 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[387]) ).
thf(417,plain,
! [SV93: term,SV34: term > $o] :
( ( ( SV34 @ SV93 )
= $true )
| ( ( SV34 @ ( lam @ ( sK35_SY346 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( ap @ ( sK19_SY344 @ SV34 ) @ ( sK23_SY391 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(418,plain,
! [SV79: term,SV88: term,SV94: subst,SV24: term > $o] :
( ( ( ~ ! [SY420: term] :
( ~ ( var @ SY420 )
| ( SV24 @ ( sub @ SY420 @ SV94 ) ) )
| ( SV24 @ ( sub @ SV88 @ SV94 ) ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK25_SY314 @ SV24 ) @ ( push @ SV79 @ id ) ) )
= $true )
| ( ( SV24 @ SV79 )
= $false )
| ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(419,plain,
! [SV24: term > $o,SV80: subst,SV77: term] :
( ( ( ~ ( var @ ( sK42_SY404 @ SV77 @ SV80 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV77 @ SV80 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK25_SY314 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[391]) ).
thf(420,plain,
! [SV80: subst,SV77: term,SV24: term > $o] :
( ( ( SV24 @ ( sub @ ( sK42_SY404 @ SV77 @ SV80 @ SV24 ) @ SV80 ) )
= $false )
| ( ( SV24 @ ( sub @ SV77 @ SV80 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK25_SY314 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[391]) ).
thf(421,plain,
! [SV84: term,SV95: term,SV24: term > $o] :
( ( ( ! [SY421: subst] :
( ~ ! [SY318: term] :
( ~ ( var @ SY318 )
| ( SV24 @ ( sub @ SY318 @ SY421 ) ) )
| ( SV24 @ ( sub @ SV95 @ SY421 ) ) ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK30_SY314 @ SV24 ) @ ( push @ SV84 @ id ) ) )
= $true )
| ( ( SV24 @ SV84 )
= $false )
| ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(422,plain,
! [SV24: term > $o,SV85: subst,SV81: term] :
( ( ( ~ ( var @ ( sK46_SY408 @ SV81 @ SV85 @ SV24 ) )
| ( SV24 @ ( sub @ ( sK46_SY408 @ SV81 @ SV85 @ SV24 ) @ SV85 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV81 @ SV85 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK30_SY314 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[393]) ).
thf(423,plain,
! [SV82: term,SV89: term,SV96: subst,SV24: term > $o] :
( ( ( ~ ! [SY423: term] :
( ~ ( var @ SY423 )
| ( SV24 @ ( sub @ SY423 @ SV96 ) ) )
| ( SV24 @ ( sub @ SV89 @ SV96 ) ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK26_SY314 @ SV24 ) @ ( push @ SV82 @ id ) ) )
= $true )
| ( ( SV24 @ SV82 )
= $false )
| ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(424,plain,
! [SV24: term > $o,SV83: subst,SV78: term] :
( ( ( ~ ( var @ ( sK43_SY407 @ SV78 @ SV83 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV78 @ SV83 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK26_SY314 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[395]) ).
thf(425,plain,
! [SV83: subst,SV78: term,SV24: term > $o] :
( ( ( SV24 @ ( sub @ ( sK43_SY407 @ SV78 @ SV83 @ SV24 ) @ SV83 ) )
= $false )
| ( ( SV24 @ ( sub @ SV78 @ SV83 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK26_SY314 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[395]) ).
thf(426,plain,
! [SV29: term > $o] :
( ( ( SV29 @ ( sK36_SY329 @ SV29 ) )
= $true )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK20_SY327 @ SV29 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[396]) ).
thf(427,plain,
! [SV97: term,SV29: term > $o] :
( ( ( SV29 @ SV97 )
= $true )
| ( ( SV29 @ ( lam @ ( sK36_SY329 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK20_SY327 @ SV29 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(428,plain,
! [SV29: term > $o] :
( ( ( ~ ( SV29 @ ( sK44_SY329 @ SV29 ) ) )
= $false )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK27_SY392 @ SV29 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[398]) ).
thf(429,plain,
! [SV29: term > $o] :
( ( ( SV29 @ ( lam @ ( sK44_SY329 @ SV29 ) ) )
= $false )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK27_SY392 @ SV29 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[398]) ).
thf(430,plain,
! [SV29: term > $o] :
( ( ( SV29 @ ( sK37_SY329 @ SV29 ) )
= $true )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( ap @ ( sK20_SY327 @ SV29 ) @ ( sK27_SY392 @ SV29 ) ) )
= $false )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[399]) ).
thf(431,plain,
! [SV98: term,SV29: term > $o] :
( ( ( SV29 @ SV98 )
= $true )
| ( ( SV29 @ ( lam @ ( sK37_SY329 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( ap @ ( sK20_SY327 @ SV29 ) @ ( sK27_SY392 @ SV29 ) ) )
= $false )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(432,plain,
! [SV99: term,SV29: term > $o] :
( ( ( SV29 @ SV99 )
= $true )
| ( ( SV29 @ ( sK32_SY329 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sK18_SY327 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(433,plain,
! [SV29: term > $o] :
( ( ( SV29 @ ( sK38_SY329 @ SV29 ) )
= $true )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK21_SY390 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[403]) ).
thf(434,plain,
! [SV100: term,SV29: term > $o] :
( ( ( SV29 @ SV100 )
= $true )
| ( ( SV29 @ ( lam @ ( sK38_SY329 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK21_SY390 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(435,plain,
! [SV101: term,SV29: term > $o] :
( ( ( SV29 @ SV101 )
= $true )
| ( ( SV29 @ ( sK33_SY329 @ SV29 ) )
= $true )
| ( ( SV29 @ ( ap @ ( sK18_SY327 @ SV29 ) @ ( sK21_SY390 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(436,plain,
! [SV34: term > $o] :
( ( ( ! [SY412: term] :
( ~ ( SV34 @ SY412 )
| ( SV34 @ ( sub @ ( sK39_SY346 @ SV34 ) @ ( push @ SY412 @ id ) ) ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK22_SY344 @ SV34 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[407]) ).
thf(437,plain,
! [SV102: term,SV34: term > $o] :
( ( ( SV34 @ SV102 )
= $true )
| ( ( SV34 @ ( lam @ ( sK39_SY346 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK22_SY344 @ SV34 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(438,plain,
! [SV34: term > $o] :
( ( ( ~ ! [SY419: term] :
( ~ ( SV34 @ SY419 )
| ( SV34 @ ( sub @ ( sK45_SY346 @ SV34 ) @ ( push @ SY419 @ id ) ) ) ) )
= $false )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK28_SY393 @ SV34 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[409]) ).
thf(439,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( lam @ ( sK45_SY346 @ SV34 ) ) )
= $false )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK28_SY393 @ SV34 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[409]) ).
thf(440,plain,
! [SV34: term > $o] :
( ( ( ! [SY413: term] :
( ~ ( SV34 @ SY413 )
| ( SV34 @ ( sub @ ( sK40_SY346 @ SV34 ) @ ( push @ SY413 @ id ) ) ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK22_SY344 @ SV34 ) @ ( sK28_SY393 @ SV34 ) ) )
= $false )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[410]) ).
thf(441,plain,
! [SV103: term,SV34: term > $o] :
( ( ( SV34 @ SV103 )
= $true )
| ( ( SV34 @ ( lam @ ( sK40_SY346 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( ap @ ( sK22_SY344 @ SV34 ) @ ( sK28_SY393 @ SV34 ) ) )
= $false )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(442,plain,
! [SV104: term,SV34: term > $o] :
( ( ( ~ ( SV34 @ SV104 )
| ( SV34 @ ( sub @ ( sK34_SY346 @ SV34 ) @ ( push @ SV104 @ id ) ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK19_SY344 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(443,plain,
! [SV34: term > $o] :
( ( ( ! [SY414: term] :
( ~ ( SV34 @ SY414 )
| ( SV34 @ ( sub @ ( sK41_SY346 @ SV34 ) @ ( push @ SY414 @ id ) ) ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK23_SY391 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[414]) ).
thf(444,plain,
! [SV105: term,SV34: term > $o] :
( ( ( SV34 @ SV105 )
= $true )
| ( ( SV34 @ ( lam @ ( sK41_SY346 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK23_SY391 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(445,plain,
! [SV106: term,SV34: term > $o] :
( ( ( ~ ( SV34 @ SV106 )
| ( SV34 @ ( sub @ ( sK35_SY346 @ SV34 ) @ ( push @ SV106 @ id ) ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK19_SY344 @ SV34 ) @ ( sK23_SY391 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(446,plain,
! [SV79: term,SV88: term,SV94: subst,SV24: term > $o] :
( ( ( ~ ! [SY420: term] :
( ~ ( var @ SY420 )
| ( SV24 @ ( sub @ SY420 @ SV94 ) ) ) )
= $true )
| ( ( SV24 @ ( sub @ SV88 @ SV94 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK25_SY314 @ SV24 ) @ ( push @ SV79 @ id ) ) )
= $true )
| ( ( SV24 @ SV79 )
= $false )
| ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(447,plain,
! [SV24: term > $o,SV80: subst,SV77: term] :
( ( ( var @ ( sK42_SY404 @ SV77 @ SV80 @ SV24 ) )
= $true )
| ( ( SV24 @ ( sub @ SV77 @ SV80 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK25_SY314 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[419]) ).
thf(448,plain,
! [SV84: term,SV95: term,SV107: subst,SV24: term > $o] :
( ( ( ~ ! [SY424: term] :
( ~ ( var @ SY424 )
| ( SV24 @ ( sub @ SY424 @ SV107 ) ) )
| ( SV24 @ ( sub @ SV95 @ SV107 ) ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK30_SY314 @ SV24 ) @ ( push @ SV84 @ id ) ) )
= $true )
| ( ( SV24 @ SV84 )
= $false )
| ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(449,plain,
! [SV24: term > $o,SV85: subst,SV81: term] :
( ( ( ~ ( var @ ( sK46_SY408 @ SV81 @ SV85 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV81 @ SV85 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK30_SY314 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(450,plain,
! [SV85: subst,SV81: term,SV24: term > $o] :
( ( ( SV24 @ ( sub @ ( sK46_SY408 @ SV81 @ SV85 @ SV24 ) @ SV85 ) )
= $false )
| ( ( SV24 @ ( sub @ SV81 @ SV85 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK30_SY314 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(451,plain,
! [SV82: term,SV89: term,SV96: subst,SV24: term > $o] :
( ( ( ~ ! [SY423: term] :
( ~ ( var @ SY423 )
| ( SV24 @ ( sub @ SY423 @ SV96 ) ) ) )
= $true )
| ( ( SV24 @ ( sub @ SV89 @ SV96 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK26_SY314 @ SV24 ) @ ( push @ SV82 @ id ) ) )
= $true )
| ( ( SV24 @ SV82 )
= $false )
| ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(452,plain,
! [SV24: term > $o,SV83: subst,SV78: term] :
( ( ( var @ ( sK43_SY407 @ SV78 @ SV83 @ SV24 ) )
= $true )
| ( ( SV24 @ ( sub @ SV78 @ SV83 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK26_SY314 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[424]) ).
thf(453,plain,
! [SV108: term,SV29: term > $o] :
( ( ( SV29 @ SV108 )
= $true )
| ( ( SV29 @ ( sK36_SY329 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sK20_SY327 @ SV29 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(454,plain,
! [SV29: term > $o] :
( ( ( SV29 @ ( sK44_SY329 @ SV29 ) )
= $true )
| ( ( ! [SY330: term] : ( SV29 @ SY330 ) )
= $true )
| ( ( SV29 @ ( sK27_SY392 @ SV29 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[428]) ).
thf(455,plain,
! [SV109: term,SV29: term > $o] :
( ( ( SV29 @ SV109 )
= $true )
| ( ( SV29 @ ( lam @ ( sK44_SY329 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK27_SY392 @ SV29 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(456,plain,
! [SV110: term,SV29: term > $o] :
( ( ( SV29 @ SV110 )
= $true )
| ( ( SV29 @ ( sK37_SY329 @ SV29 ) )
= $true )
| ( ( SV29 @ ( ap @ ( sK20_SY327 @ SV29 ) @ ( sK27_SY392 @ SV29 ) ) )
= $false )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(457,plain,
! [SV111: term,SV29: term > $o] :
( ( ( SV29 @ SV111 )
= $true )
| ( ( SV29 @ ( sK38_SY329 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sK21_SY390 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sK7_SY326 @ SV29 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(458,plain,
! [SV112: term,SV34: term > $o] :
( ( ( ~ ( SV34 @ SV112 )
| ( SV34 @ ( sub @ ( sK39_SY346 @ SV34 ) @ ( push @ SV112 @ id ) ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK22_SY344 @ SV34 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(459,plain,
! [SV34: term > $o] :
( ( ( ! [SY419: term] :
( ~ ( SV34 @ SY419 )
| ( SV34 @ ( sub @ ( sK45_SY346 @ SV34 ) @ ( push @ SY419 @ id ) ) ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK28_SY393 @ SV34 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[438]) ).
thf(460,plain,
! [SV113: term,SV34: term > $o] :
( ( ( SV34 @ SV113 )
= $true )
| ( ( SV34 @ ( lam @ ( sK45_SY346 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK28_SY393 @ SV34 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(461,plain,
! [SV114: term,SV34: term > $o] :
( ( ( ~ ( SV34 @ SV114 )
| ( SV34 @ ( sub @ ( sK40_SY346 @ SV34 ) @ ( push @ SV114 @ id ) ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK22_SY344 @ SV34 ) @ ( sK28_SY393 @ SV34 ) ) )
= $false )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(462,plain,
! [SV104: term,SV34: term > $o] :
( ( ( ~ ( SV34 @ SV104 ) )
= $true )
| ( ( SV34 @ ( sub @ ( sK34_SY346 @ SV34 ) @ ( push @ SV104 @ id ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK19_SY344 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[442]) ).
thf(463,plain,
! [SV115: term,SV34: term > $o] :
( ( ( ~ ( SV34 @ SV115 )
| ( SV34 @ ( sub @ ( sK41_SY346 @ SV34 ) @ ( push @ SV115 @ id ) ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK23_SY391 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(464,plain,
! [SV106: term,SV34: term > $o] :
( ( ( ~ ( SV34 @ SV106 ) )
= $true )
| ( ( SV34 @ ( sub @ ( sK35_SY346 @ SV34 ) @ ( push @ SV106 @ id ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK19_SY344 @ SV34 ) @ ( sK23_SY391 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[445]) ).
thf(465,plain,
! [SV79: term,SV88: term,SV94: subst,SV24: term > $o] :
( ( ( ! [SY420: term] :
( ~ ( var @ SY420 )
| ( SV24 @ ( sub @ SY420 @ SV94 ) ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV88 @ SV94 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK25_SY314 @ SV24 ) @ ( push @ SV79 @ id ) ) )
= $true )
| ( ( SV24 @ SV79 )
= $false )
| ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(466,plain,
! [SV84: term,SV95: term,SV107: subst,SV24: term > $o] :
( ( ( ~ ! [SY424: term] :
( ~ ( var @ SY424 )
| ( SV24 @ ( sub @ SY424 @ SV107 ) ) ) )
= $true )
| ( ( SV24 @ ( sub @ SV95 @ SV107 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK30_SY314 @ SV24 ) @ ( push @ SV84 @ id ) ) )
= $true )
| ( ( SV24 @ SV84 )
= $false )
| ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[448]) ).
thf(467,plain,
! [SV24: term > $o,SV85: subst,SV81: term] :
( ( ( var @ ( sK46_SY408 @ SV81 @ SV85 @ SV24 ) )
= $true )
| ( ( SV24 @ ( sub @ SV81 @ SV85 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK30_SY314 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[449]) ).
thf(468,plain,
! [SV82: term,SV89: term,SV96: subst,SV24: term > $o] :
( ( ( ! [SY423: term] :
( ~ ( var @ SY423 )
| ( SV24 @ ( sub @ SY423 @ SV96 ) ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV89 @ SV96 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK26_SY314 @ SV24 ) @ ( push @ SV82 @ id ) ) )
= $true )
| ( ( SV24 @ SV82 )
= $false )
| ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(469,plain,
! [SV116: term,SV29: term > $o] :
( ( ( SV29 @ SV116 )
= $true )
| ( ( SV29 @ ( sK44_SY329 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sK27_SY392 @ SV29 ) )
= $true )
| ( ( var @ ( sK7_SY326 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(470,plain,
! [SV112: term,SV34: term > $o] :
( ( ( ~ ( SV34 @ SV112 ) )
= $true )
| ( ( SV34 @ ( sub @ ( sK39_SY346 @ SV34 ) @ ( push @ SV112 @ id ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK22_SY344 @ SV34 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[458]) ).
thf(471,plain,
! [SV117: term,SV34: term > $o] :
( ( ( ~ ( SV34 @ SV117 )
| ( SV34 @ ( sub @ ( sK45_SY346 @ SV34 ) @ ( push @ SV117 @ id ) ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK28_SY393 @ SV34 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(472,plain,
! [SV114: term,SV34: term > $o] :
( ( ( ~ ( SV34 @ SV114 ) )
= $true )
| ( ( SV34 @ ( sub @ ( sK40_SY346 @ SV34 ) @ ( push @ SV114 @ id ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK22_SY344 @ SV34 ) @ ( sK28_SY393 @ SV34 ) ) )
= $false )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(473,plain,
! [SV104: term,SV34: term > $o] :
( ( ( SV34 @ SV104 )
= $false )
| ( ( SV34 @ ( sub @ ( sK34_SY346 @ SV34 ) @ ( push @ SV104 @ id ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK19_SY344 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(474,plain,
! [SV115: term,SV34: term > $o] :
( ( ( ~ ( SV34 @ SV115 ) )
= $true )
| ( ( SV34 @ ( sub @ ( sK41_SY346 @ SV34 ) @ ( push @ SV115 @ id ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK23_SY391 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(475,plain,
! [SV106: term,SV34: term > $o] :
( ( ( SV34 @ SV106 )
= $false )
| ( ( SV34 @ ( sub @ ( sK35_SY346 @ SV34 ) @ ( push @ SV106 @ id ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK19_SY344 @ SV34 ) @ ( sK23_SY391 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(476,plain,
! [SV24: term > $o,SV94: subst,SV88: term,SV79: term] :
( ( ( ~ ( var @ ( sK47_SY420 @ SV79 @ SV88 @ SV94 @ SV24 ) )
| ( SV24 @ ( sub @ ( sK47_SY420 @ SV79 @ SV88 @ SV94 @ SV24 ) @ SV94 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV88 @ SV94 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK25_SY314 @ SV24 ) @ ( push @ SV79 @ id ) ) )
= $true )
| ( ( SV24 @ SV79 )
= $false )
| ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[465]) ).
thf(477,plain,
! [SV84: term,SV95: term,SV107: subst,SV24: term > $o] :
( ( ( ! [SY424: term] :
( ~ ( var @ SY424 )
| ( SV24 @ ( sub @ SY424 @ SV107 ) ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV95 @ SV107 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK30_SY314 @ SV24 ) @ ( push @ SV84 @ id ) ) )
= $true )
| ( ( SV24 @ SV84 )
= $false )
| ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(478,plain,
! [SV24: term > $o,SV96: subst,SV89: term,SV82: term] :
( ( ( ~ ( var @ ( sK48_SY423 @ SV82 @ SV89 @ SV96 @ SV24 ) )
| ( SV24 @ ( sub @ ( sK48_SY423 @ SV82 @ SV89 @ SV96 @ SV24 ) @ SV96 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV89 @ SV96 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK26_SY314 @ SV24 ) @ ( push @ SV82 @ id ) ) )
= $true )
| ( ( SV24 @ SV82 )
= $false )
| ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[468]) ).
thf(479,plain,
! [SV112: term,SV34: term > $o] :
( ( ( SV34 @ SV112 )
= $false )
| ( ( SV34 @ ( sub @ ( sK39_SY346 @ SV34 ) @ ( push @ SV112 @ id ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK22_SY344 @ SV34 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(480,plain,
! [SV117: term,SV34: term > $o] :
( ( ( ~ ( SV34 @ SV117 ) )
= $true )
| ( ( SV34 @ ( sub @ ( sK45_SY346 @ SV34 ) @ ( push @ SV117 @ id ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK28_SY393 @ SV34 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(481,plain,
! [SV114: term,SV34: term > $o] :
( ( ( SV34 @ SV114 )
= $false )
| ( ( SV34 @ ( sub @ ( sK40_SY346 @ SV34 ) @ ( push @ SV114 @ id ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK22_SY344 @ SV34 ) @ ( sK28_SY393 @ SV34 ) ) )
= $false )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(482,plain,
! [SV104: term,SV118: term,SV34: term > $o] :
( ( ( SV34 @ SV118 )
= $true )
| ( ( SV34 @ ( sub @ ( sK34_SY346 @ SV34 ) @ ( push @ SV104 @ id ) ) )
= $true )
| ( ( SV34 @ SV104 )
= $false )
| ( ( SV34 @ ( sK19_SY344 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(483,plain,
! [SV115: term,SV34: term > $o] :
( ( ( SV34 @ SV115 )
= $false )
| ( ( SV34 @ ( sub @ ( sK41_SY346 @ SV34 ) @ ( push @ SV115 @ id ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK23_SY391 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(484,plain,
! [SV106: term,SV119: term,SV34: term > $o] :
( ( ( SV34 @ SV119 )
= $true )
| ( ( SV34 @ ( sub @ ( sK35_SY346 @ SV34 ) @ ( push @ SV106 @ id ) ) )
= $true )
| ( ( SV34 @ SV106 )
= $false )
| ( ( SV34 @ ( ap @ ( sK19_SY344 @ SV34 ) @ ( sK23_SY391 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(485,plain,
! [SV24: term > $o,SV94: subst,SV88: term,SV79: term] :
( ( ( ~ ( var @ ( sK47_SY420 @ SV79 @ SV88 @ SV94 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV88 @ SV94 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK25_SY314 @ SV24 ) @ ( push @ SV79 @ id ) ) )
= $true )
| ( ( SV24 @ SV79 )
= $false )
| ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(486,plain,
! [SV94: subst,SV88: term,SV79: term,SV24: term > $o] :
( ( ( SV24 @ ( sub @ ( sK47_SY420 @ SV79 @ SV88 @ SV94 @ SV24 ) @ SV94 ) )
= $false )
| ( ( SV24 @ ( sub @ SV88 @ SV94 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK25_SY314 @ SV24 ) @ ( push @ SV79 @ id ) ) )
= $true )
| ( ( SV24 @ SV79 )
= $false )
| ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(487,plain,
! [SV24: term > $o,SV107: subst,SV95: term,SV84: term] :
( ( ( ~ ( var @ ( sK49_SY424 @ SV84 @ SV95 @ SV107 @ SV24 ) )
| ( SV24 @ ( sub @ ( sK49_SY424 @ SV84 @ SV95 @ SV107 @ SV24 ) @ SV107 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV95 @ SV107 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK30_SY314 @ SV24 ) @ ( push @ SV84 @ id ) ) )
= $true )
| ( ( SV24 @ SV84 )
= $false )
| ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[477]) ).
thf(488,plain,
! [SV24: term > $o,SV96: subst,SV89: term,SV82: term] :
( ( ( ~ ( var @ ( sK48_SY423 @ SV82 @ SV89 @ SV96 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV89 @ SV96 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK26_SY314 @ SV24 ) @ ( push @ SV82 @ id ) ) )
= $true )
| ( ( SV24 @ SV82 )
= $false )
| ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(489,plain,
! [SV96: subst,SV89: term,SV82: term,SV24: term > $o] :
( ( ( SV24 @ ( sub @ ( sK48_SY423 @ SV82 @ SV89 @ SV96 @ SV24 ) @ SV96 ) )
= $false )
| ( ( SV24 @ ( sub @ SV89 @ SV96 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK26_SY314 @ SV24 ) @ ( push @ SV82 @ id ) ) )
= $true )
| ( ( SV24 @ SV82 )
= $false )
| ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(490,plain,
! [SV112: term,SV120: term,SV34: term > $o] :
( ( ( SV34 @ SV120 )
= $true )
| ( ( SV34 @ ( sub @ ( sK39_SY346 @ SV34 ) @ ( push @ SV112 @ id ) ) )
= $true )
| ( ( SV34 @ SV112 )
= $false )
| ( ( SV34 @ ( sK22_SY344 @ SV34 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(491,plain,
! [SV117: term,SV34: term > $o] :
( ( ( SV34 @ SV117 )
= $false )
| ( ( SV34 @ ( sub @ ( sK45_SY346 @ SV34 ) @ ( push @ SV117 @ id ) ) )
= $true )
| ( ( ! [SY348: term] : ( SV34 @ SY348 ) )
= $true )
| ( ( SV34 @ ( sK28_SY393 @ SV34 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(492,plain,
! [SV114: term,SV121: term,SV34: term > $o] :
( ( ( SV34 @ SV121 )
= $true )
| ( ( SV34 @ ( sub @ ( sK40_SY346 @ SV34 ) @ ( push @ SV114 @ id ) ) )
= $true )
| ( ( SV34 @ SV114 )
= $false )
| ( ( SV34 @ ( ap @ ( sK22_SY344 @ SV34 ) @ ( sK28_SY393 @ SV34 ) ) )
= $false )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(493,plain,
! [SV115: term,SV122: term,SV34: term > $o] :
( ( ( SV34 @ SV122 )
= $true )
| ( ( SV34 @ ( sub @ ( sK41_SY346 @ SV34 ) @ ( push @ SV115 @ id ) ) )
= $true )
| ( ( SV34 @ SV115 )
= $false )
| ( ( SV34 @ ( sK23_SY391 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK8_SY343 @ SV34 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(494,plain,
! [SV24: term > $o,SV94: subst,SV88: term,SV79: term] :
( ( ( var @ ( sK47_SY420 @ SV79 @ SV88 @ SV94 @ SV24 ) )
= $true )
| ( ( SV24 @ ( sub @ SV88 @ SV94 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK25_SY314 @ SV24 ) @ ( push @ SV79 @ id ) ) )
= $true )
| ( ( SV24 @ SV79 )
= $false )
| ( ( SV24 @ ( sK6_SY312 @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[485]) ).
thf(495,plain,
! [SV24: term > $o,SV107: subst,SV95: term,SV84: term] :
( ( ( ~ ( var @ ( sK49_SY424 @ SV84 @ SV95 @ SV107 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV95 @ SV107 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK30_SY314 @ SV24 ) @ ( push @ SV84 @ id ) ) )
= $true )
| ( ( SV24 @ SV84 )
= $false )
| ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[487]) ).
thf(496,plain,
! [SV107: subst,SV95: term,SV84: term,SV24: term > $o] :
( ( ( SV24 @ ( sub @ ( sK49_SY424 @ SV84 @ SV95 @ SV107 @ SV24 ) @ SV107 ) )
= $false )
| ( ( SV24 @ ( sub @ SV95 @ SV107 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK30_SY314 @ SV24 ) @ ( push @ SV84 @ id ) ) )
= $true )
| ( ( SV24 @ SV84 )
= $false )
| ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[487]) ).
thf(497,plain,
! [SV24: term > $o,SV96: subst,SV89: term,SV82: term] :
( ( ( var @ ( sK48_SY423 @ SV82 @ SV89 @ SV96 @ SV24 ) )
= $true )
| ( ( SV24 @ ( sub @ SV89 @ SV96 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK26_SY314 @ SV24 ) @ ( push @ SV82 @ id ) ) )
= $true )
| ( ( SV24 @ SV82 )
= $false )
| ( ( SV24 @ ( ap @ ( sK6_SY312 @ SV24 ) @ ( sK12_SY380 @ SV24 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[488]) ).
thf(498,plain,
! [SV117: term,SV123: term,SV34: term > $o] :
( ( ( SV34 @ SV123 )
= $true )
| ( ( SV34 @ ( sub @ ( sK45_SY346 @ SV34 ) @ ( push @ SV117 @ id ) ) )
= $true )
| ( ( SV34 @ SV117 )
= $false )
| ( ( SV34 @ ( sK28_SY393 @ SV34 ) )
= $true )
| ( ( var @ ( sK8_SY343 @ SV34 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(499,plain,
! [SV24: term > $o,SV107: subst,SV95: term,SV84: term] :
( ( ( var @ ( sK49_SY424 @ SV84 @ SV95 @ SV107 @ SV24 ) )
= $true )
| ( ( SV24 @ ( sub @ SV95 @ SV107 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK30_SY314 @ SV24 ) @ ( push @ SV84 @ id ) ) )
= $true )
| ( ( SV24 @ SV84 )
= $false )
| ( ( SV24 @ ( sK12_SY380 @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[495]) ).
thf(500,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[65,499,498,497,496,494,493,492,490,489,486,484,482,469,467,460,457,456,455,453,452,450,447,444,441,437,435,434,432,431,427,425,420,417,413,406,402,389,340,320,318,297,295,255,228,224,223,218,213,191,190,188,182,169,164,163,162,161,160,159,158,139,138,136,132,110,107,103,102,98,97,95,67]) ).
thf(501,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[500]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG261^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.17 % Computer : n014.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 18:09:26 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.19/0.39
% 1.19/0.39 No.of.Axioms: 0
% 1.19/0.39
% 1.19/0.39 Length.of.Defs: 38205
% 1.19/0.39
% 1.19/0.39 Contains.Choice.Funs: false
% 1.19/0.39 ...................
% 1.19/0.39
% 1.19/0.39 ********************************
% 1.19/0.39 * All subproblems solved! *
% 1.19/0.39 ********************************
% 1.19/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:36,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:500,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.19/0.39
% 1.19/0.39 %**** Beginning of derivation protocol ****
% 1.19/0.39 % SZS output start CNFRefutation
% See solution above
% 1.19/0.40
% 1.19/0.40 %**** End of derivation protocol ****
% 1.19/0.40 %**** no. of clauses in derivation: 501 ****
% 1.19/0.40 %**** clause counter: 500 ****
% 1.19/0.40
% 1.19/0.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:36,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:500,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------